Post on 14-Apr-2018
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Kunci Penyelesaian Matematika SMA Jl.2A- Sukino Bab 3 | page 51
Latihan Kompetensi Siswa 1
A. Evaluasi Pengertian atau Ingatan
1. C. xx sincos32
1
30cos x = 30sinsin30coscos xx
=2
1.sin3
2
1.cos xx
= xx sincos32
1
2. A. xx sincos22
1
45cos x = 45sinsin45coscos xx
= xx sincos22
1
3. A. 1321 75cos = 4530cos
= 45sin30sin45cos30cos
= 221.
212
21.3
21
= 1321
4. A.22
13
15cos = 4560cos= 45sin60sin45cos60cos
= 21
.32
12
1.
2
1
= 2
231241
=22
13
5. C. yx22
sincos
yxyx coscos = yxyx sinsincoscos yxyx sinsincoscos
= yxyx2222
sinsincoscos
= yxyx 2222 sincos1sin1cos = yx
22sincos
6. A. 60cos x
xx cos2
1sin3
2
1 = xx cos60cossin60sin
= 60cos x
7. B. -0,5
cos = sinsincoscos
=14
35.
34
14
11.
7
1
= 5,098
49
8
6011
8. D.2
12
13
2
1aa
3cos
=
3sinsin
3coscos
= 3
2
1.
2
1.1
2aa
9. A. 1
35sin125sin35cos125cos = 35125cos= 90cos = 1
10. B.5
3
cos = sinsincoscos
=5
3.
25
7
5
4.
25
24
= 5.25
75
= 5
3
11. E.125
117
cos = sinsincoscos
=25
7.
5
3
5
4.
25
24 =
125
117
12. D.2
1
BA cos = BABA sinsincoscos
= 0.2
31.
2
1 =
2
1
13. E. x7cos
xxxx 3cos4cos3sin.4sin = xx 34cos = x7cos
BAB 3
RUMUS RUMUS
TRIGONOMETRI
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Kunci Penyelesaian Matematika SMA Jl.2A- Sukino Bab 3 | page 52
14. B. 3122
1
22
1cos P 45P
32
1cos Q 30Q
R = 105180 QP
105coscosR = 4560cos= 45sin60sin45cos60cos
= 22
1.3
12
2
1.
2
1
= 3124
1
15. B.5
13
Ccos = BA 180cos= BABA sin180sincos180cos
= BABA
sin.0cos.1= BABA sinsincoscos
=
17
15.
5
3
17
8.
5
4
=85
13
B. Evaluasi Pemahaman dan PenguasaanMateri
1. a. ba 32cos = baba 3sin2sin3cos2cosb. yx3cos = yxyx sin3sincos3cos
c. 45cos x = 45sinsin45coscos xx
= xx sincos22
1
d. 15cos x = 15sinsin15coscos xx
e.
3cos2
x = 2
3sinsin
3coscos
xx
= 2
xx sin3
2
1cos
2
1
= xx sin3cos22
1
f.
6cos32 x = 32
6sinsin
6coscos xx
= 32
xx sin
2
1cos3
2
1
= 3 xx sincos3
g.
BA
2
1
3
1cos =
= BABA2
1sin
3
1sin
2
1cos
3
1cos
h.
BA
4
1
3
2cos =
= BABA1
sin3
2sin
1cos
2cos
2. a. x90cos = xx sin90sincos90cos = xx sin.1cos.0
= xsin
b. x270cos = xx sin270sincos270cos = xx sin.1cos.0= xsin
c. x270cos = xx sin270sincos270cos = xx sin.1cos.0= xsin
d. 90cos x = 90sinsin90coscos xx = xx sin.1cos.0
= xsin
e. 180cos x = 180sinsin180coscos xx = xx sin.0cos.1
= xcos
f.
5
2cos =
=
5sin2
sin5cos2
cos
= 5sin.15cos.0 = 5sin
g.
2
3cos =
2
3sinsin
2
3coscos
= sin.1cos.0 = sin
h. 2cos = sin2sincos2cos = sin.0cos.1
= cos
3. a.3
sin3
sin3
cos3
cos
=
33
cos
= 1
b.6
sin3
sin6
cos3
cos
=
63
cos
=
2cos
= 0
c.4
sin3
2sin
4cos
3
2cos
=
43
2cos
=
12
11
cos
d.3
sin5
sin3
cos3
5cos
=
4
3
3
5cos
=
12
29cos
e. 60sin50sin60cos50cos = 110cos
f. 30sin40sin30cos40cos = 70cos
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4. a. 60sin180sin60cos180cos == 60180cos
=2
1
b. 90sin150sin90cos150cos == 240cos
= 240cos= 60180cos
= -2
1
c. 10sin140sin10cos140cos =
= 10140cos= 150cos
= -2
13
d. 20sin200sin20cos200cos =
= 20200cos= 180cos= -1
5. a. cos = sinsincoscos
=13
5.
5
3
13
12.
5
4
=5
63
b. cos = sinsincoscos
=
13
5.
5
3
13
12.
5
4
=5
33
c. cos = sinsincoscos
=
13
5.
5
3
13
12.
5
4
=5
33
d. cos = sinsincoscos
=
13
5.
5
3
13
12.
5
4
=5
33
e.
2cos =
sin
2sincos
2cos
= sin.1cos.0
= sin
f.
2cos =
sin
2sincoscos
= sin.1cos.0
= sin
g.
4cos =
sinsincoscos
= sin.22
1cos.2
2
1
= sincos22
1
h.
6cos = sin
6sincos
6cos
= sin.2
1cos.3
2
1
= sincos32
1
7. a. BA cos = BABA sinsincoscos = 32
1
=2
1coscos BA = 3
2
1
= BAcoscos = 132
1
b. BA cos = BABA sinsincoscos
= 2
113
2
1
= 2321
8. a. BA cos = BABA sinsincoscos
=10
9.
10
1
10
19.
10
99
=100
91881
b. BA cos = BABA sinsincoscos
=10
9.
10
1
10
19.
10
99
=100
91881
c. BA cos = BABA sinsincoscos
=10
9.
10
1
10
19.
10
99
=100
91881
d. BA cos = BABA sinsincoscos
=10
9.
10
1
10
19.
10
99
=100
91881
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e. BA cos = BABA sinsincoscos
=10
9.
10
1
10
19.
10
99
=100
91881
f.
BAcos = BABA sinsincoscos
=10
9.
10
1
10
19.
10
99
=100
91881
9. a. BA cos = BABA sinsincoscos
=13
5.
25
24
13
12.
25
7
=325
204
b. BA cos = BABA sinsincoscos
=13
5.
25
24
13
12.
25
7
=325
36
c. BA cos = BABA sinsincoscos
=13
5.
25
24
13
12.
25
7
=325
204
d. BA
cos = BABA sinsincoscos
=13
5.
25
24
13
12.
25
7
=325
36
10. a. BA cos = BABA sinsincoscos
=5
3.
13
12
5
4.
13
5
=65
16
b. BA cos = BABA sinsincoscos
=5
3.
13
12
5
4.
13
5
=5
56
11. a. 22 sinsincoscos BABA
=BABA
BABA
sinsin2sinsin
coscos2coscos
22
22
= BABA
BABA
sinsincoscos2
sinsincoscos 2222
= BA cos22
b. BA cos . BA cos
= BABA
BABA
sinsincoscos
sinsincoscos
= BABA 2222 sinsincoscos
= BABA 2222 cos1sincossin1 = AB 22 sincos
12. 222
1QP = 22 coscossinsin
2
1yxyx
=
yxyx
yxyx
sinsincoscos2
coscossinsin
2
1 2222
= yx cos222
1
= 1 + cos(x y)
13. 45cos2 x = 45cos x= 45sinsin45coscos2 xx =
45sinsin45coscos xx
= 45coscos x = 45sinsin3 x
a.x
xx
cos
sintan =
45sin3
45cos=
3
1
b.x
xsin
coscot =
1
3= 3
c. x30cos = xx sin30sincos30cos
= xx sin2
1cos3
2
1
= xx sincos32
1
d. 30cos x = 30sinsin30coscos xx
= xx sin2
1cos3
2
1
= xx sincos32
1
14.
t
t
30cos
30cos=
t
tt
sin30sincos30cos
sin30sincos30cos
tt sin2
1cos3
2
1 =
ttn sin
2
1cos3
2
1
nt 1cos321
= 1sin21
nt
tt
cos
sintan =
1
13
21
21
n
n
= n
n
1
13
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15. a.
3
4cos
3
2coscos AAA
=
3
4sinsin
3
4coscos
3
2sinsin
3
2coscoscos
AA
AAA
=
AA
AAA
sin32
1cos
2
1
sin321cos
21cos
= 0
b. cos + cos = sinsincoscos +
sinsincoscos
= coscos2
c. cos - cos = sinsincoscos -
sinsincoscos = sinsin2
C. Evaluasi Kemampuan Analisis
1. cos = 2 cos= sinsincoscos =
2 sinsincoscos = sinsin3coscos
=
cos
sin.
cos
sintan.tan =
3
1
2.
3cos
=
3sinsin
3coscos
= sin32
1cos
2
1 =
1..(1)
3cos
=
3sinsin
3coscos
= sin32
1cos
2
1 =
14
11..(2)
(1) dan (2)
sin321cos
21 = 7
1
sin32
1cos
2
1 =
14
11
+
14
13cos
3. cos + cos = sinsincoscoscos
= sinsincoscos180cos = sinsincoscoscos
=
sinsincoscos
sinsincoscos
= sinsin2
4. a.
BA
BA
coscos
cos=
BA
BABA
coscos
sinsincoscos
= BA tantan1
b. A
BA
sinsin
cos=
BA
BABA
sinsin
sinsincoscos
= 1cotcot BA
c.
BA
BA
coscos
cos=
A
BABA
coscos
sinsincoscos
= BA tantan1
d. A
BAsinsin
cos =BA
BABAsinsin
sinsincoscos
= 1cotcot BA
e.
BA
BA
sinsin
cos
=
A
BABA
sinsin
sinsincoscos
= BA cotcot1
f.A
BA
cossin
cos =
A
BABA
cossin
sinsincoscos
= BA tan11.cot
= BA tancot
g.
BA
BA
cossin
cos
=
BA
BABA
cosin
sinsincoscos
= BA tancot= AB cottan
h. BA
sinsin
cos
=
A
BABA
sinsin
sinsincoscos
= 1cotcot BA
= - BAcotcot1
8. a.
3
cos4
x =
3
sinsin3
coscos4
xx
=
xx sin3
2
1cos
2
14
= xx sin32cos2
jadi, a = 2 dan b = 32
b.
4cos2
x =
4sinsin
4coscos2
xx
=
xx sin2
2
1cos2
2
12
= xx sincos jadi, a = 1 dan b = 1
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9. a. cos.cos6sin8 r= sinsincoscos r
6cos r cos
6r
8sin r sin
8r
cos
6=
sin
8
cos
sintan =3
48
b. cos.cos3sin4 r= sinsincoscos r
3cos r cos
3r
4sin r sin
4r
cos
3=
sin
4
cos
sintan =
3
4
c. cos.sin7cos4 r= sinsincoscos r
4cos r cos
4r
7sin r sin
7r
cos
4=
sin
7
cos
sintan =
7
d. cos.cos5sin12 r= sinsincoscos r
5cos r cos
5r
12sin r sin
12r
cos
5=
sin
12
cos
sintan =
5
12
10. a.
3cos
3coscos 222
=
3cos2cos 22
=
2
2
2
12cos
= 2cos2
1
b. 222 sin60cos60cos
= 260sinsin60coscos +
2sin60sincos60cos - 2sin
=
2
sin32
1cos2
1
+
2
sin32
1cos2
1
-
2sin
= 222 sinsin2
3cos
2
1
= 22 sin2
1cos
2
1 =
2
1
c. 15sin75cos 22 =dari soal no.11b bagian B diperoleh :
15sin75cos22
= 1575cos1575cos= 60cos90cos
= 02
1.0
Latihan Kompetensi Siswa 2
A. Evaluasi Pengertian atau Ingatan
1. E. 1
11sin79cos11cos79sin = 1179sin
= 90sin = 1
2. A. 31
10sin50cos10cos50sin = 60sin
= 31
3. E. 32
1
16sin76cos16cos76sin = 60sin
= 31
4. A. xx cossin21 45sin x = 45sincos45cossin xx
= xx cossin22
1
5. A. 1626
1
30sin x = 30sincos30cossin xx
= xx cos2
1sin3
2
1
=1
.
2
1
3
22.3
2
1
= 1626
1
6. A. 30sin x
xx cos2
1sin3
2
1 = xx cos30sinsin30cos
= 30sin x
7. A.2
1 a
140sin = 5090sin= 50sin90cos50cos90sin
= 50sin.01.1 2 a
=2
1 a
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8. A.22
13
15sin = 4560sin= 45sin60cos45cos60sin
=
2
13
2
12
2
1
= 2
2132
4
1
=22
13
9. C.22
31
75sin = 3045sin= 30sin45cos30cos45sin
=
2
13
2
12
2
1
= 2
2132
4
1
=22
13
10. A. xy 22 coscos
yxyx sinsin = yxyx sincoscossin yxyx sincoscossin
= yxyx 2222 sincoscossin
= yxyx 2222 cos1coscoscos1 = xy 22 coscos
11. D. sin2
4sin
4sin =
sincoscos
4sin
sin
4coscos
4sin
=
sincos2
= sin22
1.2 = sin2
12. A.6
1
sin = sincoscossin = 30sin
=2
1sincos
3
1
6
1
sincos
13. E.125
44
BAsin = BABA sincoscossin
=25
7.
5
4
25
24.
5
3
=
125
44
14. A.221
21
BAsin = BABA sincoscossin
=17
8.
13
12
17
15.
13
5
=221
21
15. D.25
24
Csin = BA 180sin= BABA sin180coscos180sin= BA sin1= BA sin= BABA sincoscossin
=5
3.
5
4
5
4.
5
3 =
25
24
B. Evaluasi Pemahaman dan PenguasaanMateri
1. a. BA sin = 6030sin = 1
BA sin = 6030sin =2
130sin
b. BA sin = 3060sin = 1
BA sin = 3060sin =2
130sin
c. BA sin =
46sin
= sin6
cos4
cos6
sin
=
22
31
BA sin =
46sin
= sin6
coscos6
sin
=
22
31
d. BA sin = 4030sin = 70sin BA sin = 4030sin = 10sin
= 10sin
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e. BA sin =
312sin
=
12
5sin
BA sin =
312sin
=
12
3sin
=
4sin
= 2
2
1
f. BA sin =
44sin =
2sin
= 1
BA sin =
44sin = 2sin
2. a. BA sin = BABA sincoscossin
=13
5.
5
3
13
12.
5
4 =
65
63
b. BA sin = BABA sincoscossin
=13
5.
5
3
13
12.
5
4 =
65
33
c. BA sin + BA sin =65
63+
65
33=
65
98
d. BA sin - BA sin =65
63-
65
33=
65
30
e. BA sin . BA sin =65
63.
5
33=
2425
2079
f. BA
BA
sin
sin=
65
63x
33
65=
33
63
3. a. xsin = xx sincoscossin
= xx sin1cos.0 = xsinb. xsin = xx sincoscossin
= xx sin1cos.0 = xsin
c.
x
2
3sin
= xx sin
2
3coscos
2
3sin
= xx sin.0cos.1 = cos
d.
x
2
3sin
= xcos
e.
2sin
x =
2sincos
2cossin
xx
= xx cos.10.sin = xosf. xsin = sincoscossin xx
= xx cos.0sin.1 = xsin
g.
x
2sin
= xx sin
2coscos
2sin
= xx sin.0cos.1 = xos
h.
2
3sin
x =
2
3sincos
3cossin
xx
= xx cos.1sin.0 = xcos
4. a. BA
BA
sin
sin=
BABA
BABA
sincoscossin
sincoscossin
=
BA
BABABA
BABA
coscos
sincoscossincoscos
sincoscossin
= A
BA
anan
tantan
b. BA
sinsin
sin=
BABA
sinsin
sincoscossin
= AB cotcot
c.
BA
BA
sinin
sin =
BA
BABA
sinsin
sincoscossin
= AB cotcot
d.
BA
BA
coscos
sin=
BA
ABBA
coscos
cossincossin
= BA tantan
5. a. 105sin = 4560sin= 45sin60cos45cos60sin
=
2
13
2
12
2
1
= 2
2132
4
1
=22
31
b. 105sin = 105sin
=
22
31
c. 195sin = 45150sin = 45sin150cos45cos150sin
= 6090cos6090sin22
1
=4
62
d. 255sin = 45210sin= 45sin210cos45cos210sin
= 30180cos30180sin221
=
3
2
1
2
12
2
1
=62
6. a.
sinsin
coscos
=
sincoscossinsincoscossin
sinsincoscossinsincoscos
=
cossin2
coscos2= cot
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b. 2
1sin
2
1cos =
2
1sin
2
1cos
2
1cos
2
1sin
2
1cos
=
2
1sin2
1cos
2
1cos
2
1sin180
2
1cos
= 2
1sin
2
1cos
2
1cos
2
1sin
2
1sin
=
2
1sin
2
1cos
2
1cos
2
1sin
2
1sin
2
1cos
2
1cos
2
1sin
= 2
1cos
2
1sin2
7. a.
5cos
cos
5sin
sin =
5cos5in
5sincos5cossin
=
5cos5sin
6sin
b. cos + cos =
sinsincoscos + sinsincoscos
= coscos2
c. cos - cos = cossin2d. sin + sin =
sincoscossin + sincoscossin
= cossin2
e. sin - sin = sincos2
8. a. BAcossin2
dari soal no.7 (d) diperoleh :
BAcossin2 = BAsin + BA sin= 0,7 + 0,5 = 1,2
b. BAsincos2
dari soal no.7 (e) diperoleh :
BAsincos2 = BAsin - BA sin= 0,7 - 0,5 = 0,2
c. BA cos = BABA sinsincoscos = BABA coscos
2
1-
BABA coscos2
1
= BA cos = 32
1
d. BAsin = 0,5
9. cos = sinsincoscos =3
cos
= 0,1 - sinsin =21
sinsin = -0,4
a. cos = sinsincoscos = 0,1 + (-0,4) = -0,3
b. cos = sinsincoscos = 0,1 + (-0,4) = -0,3
c. sin = -0,1d. sin = -0,1
10.2
sinsincoscos BABA +2
cossinsincos BABA
=
BABABA
BABA
BABABA
22
2222
22
cossinsinsincoscos2
sincossinsin
sinsincoscos2coscos
= BBABBA 222222 cossincoscossinsin = BBAA 2222 cossincossin = 1
C. Evaluasi Kemampuan Analisis
1. a. CBA sin = CBA sin= CBACBA sincoscossin
= CBCBA
CBCBA
sincoscossincos
sinsincoscossin
=CBACBA
CBACBA
sinsinsinsincoscos
cossincoscoscossin
b. CBA cos =
CBACBA sinsincoscos=
CBACBA
CBACBA
sincossincossinsin
sinsincoscoscoscos
3. Asincos = Asincos sincoscoscossincos AA =
AA sincoscoscossincos
=
sincoscossincos
coscos2sin
A
A
= Atan =
coscos2
sincossin
AA
4. BA cos = BABA sinsincoscos =5
3
BA tantan =B
BA
coscos
sinsin= 2
BAsinsin = BAcoscos2
BA cos = BAcoscos3 =5
3
b. BAcoscos =
5
1
a. BAsinsin =5
1.2 =
5
2
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c. BA cos = BABA sinsincoscos
=5
1-
5
2=
5
1
5. a. 15sin75sin 22 = 15sin1590sin 22
= 15sin15cos 22
dari soal no.11(b) bagian B := 1515cos1515cos = 0cos30cos
= 1.2
1=
2
1
b. 75cos15cos 22 = 1590cos15cos2
= 15sin15cos 22
=2
1
7. a. BA cos = BABA sinsincoscos
=17
15.
13
5
17
15.
13
12
=
221
255
b. BA sin = BABA sincoscossin
=17
15.
13
12
17
15.
13
5
=
21
105
c. BA sin =221
255
d. BA cos =221
105
8. a. BA sin = BABA sincoscossin
=
13
12.
17
8
13
5.
17
15=
21
21
b. BA cos = BABA sinsincoscos
=
13
12.
17
15
13
5.
17
8
=221
140
c. kuadran III, karena BAsin dan BA cosbernilai negatif.
9. BftaBftay sin2coscos2sin
Bfta 2sin.
10.21
yy =
tAtA cos
2cos
21
=
2sinsin
2coscos
1
ttA +
sinsincoscos2 ttA = tA sin1 + tA cos2
= tAtA sincos 12
11. a. sinr = sincoscossin rr = cos6sin8
8cosr os
8r
6sin r sin
6r
cos
8=
in
6
cossintan = 4
3
b. sinr = sincoscossin rr
= cos3sin4
4cosr os
4r
3sin rsin
3r
cos
4=
sin
3
cos
sintan =
4
3
c. 2cosr cos
2r
3sin r sin
3r
cos
2=
sin
3
cos
sintan =
2
3
d. 12cosr os
12r
5sin r sin
5r
cos
12=
sin
5
cos
sintan =
12
5
12. a.
4sin2
x =
4sincos
4cossin2
xx
= xx cossin
b.
4sin2
x =
4sincos
4cossin2
xx
= xx cossin
c.
6sin2
x =
6sincos
6cossin2
xx
=
xx cos
2
1sin3
2
12
= xx cossin3
d.
3sin
x -
6cos
x =
=3
sincos3
cossin
xx -
6sinsin
6coscos
xx
= xxxx sincos32
1cos3sin
2
1
= xsin
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15. BABABABA cossin2cossin2= BABA sincoscossin2
BABA sinsincoscos - BABA sincoscossin2 BABA sinsincoscos
= BAABBA 22 sincossin4cossinsin4 = BAsinsin4 BABA sincoscossin = BABA sinsinsin4= CBA 180sinsinsin4= CBA sinsinsin4
Latihan Kompetensi Siswa 3
A. Evaluasi Pengertian atau Ingatan
1. C. tan (-x)
4
4
tan1
tan1
x
x=
44
44
tan.tan1
tantan
x
x
=
44tan
x
= tan (-x)
2. B. 2tan
452tan1
452tan1
=
452tan.45tan1
452tan45tan
= 45245tan
= 2tan
3. A. CBA tan4. C. CBA tan5. A. -1
66an.69an1
66tan69tan= 6669tan
= 135tan
= 45180tan = -1
6. D. 54tan
9sin9cos
9sin9cos=
9an1
9tan1=
9an.45tan1
9tan45tan
= 945tan= 54tan
7. B.
tan =
tan.tan1
tantan
= 1.1
6661
66
61
111
65
111
6
5
= 45
8. B. 34tan
11sin11cos
11sin11cos=
11an1
11tan1
=
11tan.45tan1
11tan45tan
= 1145tan= 34tan
9. B.11
BA cot = BAtantan
tan.tan1
=BA
BA antan
tan.tan
anan
1
=BAa tan
1tan
1
11
=
A cotcot
11
=11
10. D. 1
4cot .
4cot =
tantan
tan.tan1
4
4 x
tantan
tan.tan1
4
4
=
2
4
2
2
4
2
tantan
tan.tan1
=
2
2
an1
tan1
= 1
B. Evaluasi Pemahaman dan PenguasaanMateri
1. a.
115tan.155an1
115tan155tan= 115155tan
= 40tan
= 1525tan
=
15tan.25an1
15tan25tan
= 13
1313
13
.1
a
a
= 113
113
aa
aa
b.
150an.175tan1
150tan175tan= 150175tan
= 25tan = a
c. 15tan.10an1
15tan10tan= 25tan = a
d. 5,10tan.5,14tan1
5,10tan5,14tan= 25tan = a
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2. a. 15tan = 6045tan
=
60tan.5an1
60tan45tan
=31
31
b. 75tan = 75tan= 3045tan
=
30tan.45tan1
30tan45tan
=
31
31
31
31
=
33
33
c. 255tan = 75180tan
=5an180an1
75tan180tan
= 75tan
=33
33
d. 105tan = 105tan= 4560tan
=45tan.60an1
45tan60tan
=
31
13
e. 195tan = 195tan
=15tan.180an1
15tan180tan
= 15tan =
31
13=
31
31
f. 285tan = 105180tan
=105an180an1
105tan180tan
= 105tan
=31
31
g. 105tan =31
31
h. 195tan =31
13
i. 105cot =105an
1=
31
31
j. 195cot =195an
1=
13
31
3. a. BA tan =BA
BA
an.an1
tantan
= 33
56
.11533
1556
512
34
512
34
BA tan =63
16
15
63
1516
b. BA tan = 63
16
.115
63
1516
34
512
34
512
BA tan =33
56
15
33
1556
c. BA tan =6214
8213
.1214
6214
214
8213
21
243
21
243
BA tan =6214
8213
d. BA tan = 63
16
.1125
43
125
43
BA tan =33
56
4. a.
A4tan
= A
A
tan.tan1
tantan
4
4
=
A
an1
tan1
=AA
AA
sincos
sincos
b.
A
4tan
=
A
A
tan.tan1
tantan
4
4
=
A
A
an1
tan1
=AA
AA
sincos
sincos
c. A45tan . A45tan =
=AA
AA
sincos
sincos
.
AA
AA
sincos
sincos
= 1
d.
6tan =
6
6
tan.tan1tantan
=
tan.31tan3
31
31
=
tan.33
tan33
=
tan3
tan31
3
3
=
tan3
tan31
5. a. BA tan =BA
BA
an.an1
tantan
= 0,75
B
B
an21
tan2
= 0,75
BB tan5,175,0tan2
25,1tan5,2 B
Btan 0,5
b. BA tan =BA
BA
an.an1
tantan
=25
25
.171
43
71
4
3
= 1
A + B =4
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c. BA tan =A
BA
an.an1
tantan
=
3
4
21
21
.tan1
tan
A
A
=
3
4
AA tan2
3
4
2
1tan
65tan
35 A
5
3
6
5tan A = 0,5
6. a. 70tan c. 60tanb. 30tan d. 20tan
7. a. 1tan . 1tan =1tantantantan
= 1tantan
tantan1
= tantan1
2
b.
tan
tan=
tan.tan1
tantan
.
tantan
tantan1
=11
tantan
.
tantan
11
= 0
8. a.
BBAABA
tan.tan1
tantan
= ABA tan = Btan
b. BAA
BAA
tantan1
tantan= BAA tan = Btan
c. BA cot =A
BA
anan
tan.tan1
=BABA
BABA
incoscossin
sinsincoscos
x
BA
BA
sinsin1
sinsin1
=A
BA
cotot
1cot.cot
d. BA cot =BA
BA
anan
tan.tan1
= BABA
BABA
sincoscossin
sinsincoscos
x
BA
BA
sinsin1
sinsin
1
=B
BA
cotcot
1cot.cot
9. a. BA tan = 323
36
.1 512
724
512
724
b. BA tan =
253204
.1 512
724
512
724
c. sudut (A + B) di kuadran III
d. sudut (A - B) di kuadran III
10. a. BA tan =A
BA
anan1
tantan
= 21
220
.18
15125
815
125
b. BA tan = 171
140
.18
15125
815
125
c. sudut (A - B) di kuadran IIId. sudut (A + B) di kuadran IV
C. Evaluasi Kemampuan Analisis
1. A45tan = A45tan4
45an.tan1
tan45tan
A
A
=A
tan.45tan1
tan45tan.4
2tan1 A = 2tan14 A
AA tan2tan1 2 = AA tan8tan44 2
3tan10tan3 2 AA = 0
3tan1tan3 AA = 0
3
1tan A atau 3tan A
2. yx tan =yx
yx
tan.tan1
tantan
=
yx tan =
yx
yx
tan.tan1
tantan
= b
yx tantan = yxa tantan = byx tantan
=2
tantan2ba
xxba
a. x2tan =
4
2 2
1tan1
tan2ba
ba
x
x
=bba
ba
2
4422
yx tan =yx
yx
tan.tan1
tantan
=
=ya
yba
Ba
tan
tan
2
2
= a
= yba
aayba
tan2
tan2
2
2
1tan
ba
ba
a
ay
b. y2tan =
2
2
2
2
2
2
11
1.2
tan1
tan2
ba
ba
ba
ba
a
a
a
a
y
y
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3. tan =
tan.tan1
tantan
= QPQP
PQ
QP
QP
QP
121.1 11
11
= cotcot
4. a. CBA tantantan =
BABA 180tantantan
= BA tantan BA
BA
tan.180tan1
tan180tan
= BA tantanA
BA
an.an1
tantan
=BA
BABA
BABA
an.an1
tantantantan
tantantantan
2
2
= CBA tantantan
b. Ctan = BA180tan= BA tan
=A
BA
tan.an1
tantan
= 5,14,2.5,11
4,25,1
tan A = tan Cjadi, A = C
5. 0152 2 xx
0112 xx
2
11
x ; 12
x
2
1tan ; 1tan
a. tan = 31.1
1
21
2
3
21
21
b. tan =3
1
1.1
1
23
21
21
21
6. a. BA tan = BA 180tan= Ctan
=7
5
b. BA tan =B
BA
an.an1
tantan
=
7
5
=81
tantan
BA=
5
= BA tantan = 75
= 5
7. a. tan =
tan.tan1
tantan
=21
21
.1 mm
mm
b. tan =
11
21 mm
90
9. BA cot = BABA
antan
tan.tan1
=xy
xy
x
y
x
1
Latihan Kompetensi Siswa 4
A. Evaluasi Pengertian atau Ingatan
1. C. 25
7
x2cos = x2sin21
=25
321
5
421
2
=
25
7
2. B.89
240
x2sin = xx cossin2
=17
8.
17
15.2 =
289
240
3. C.169
119
x2cos = x2
sin21
=169
501
13
521
2
=
169
119
4. E.7
24
x2tan = 167
23
2
43
43
21
.2
tan1
tan2
x
x
= 241623
5. C.27
8
x3sin = xx cos2sin2
= xx 2cossin4
=
2
3
2.
3
1.4
=
27
8
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6. E. -1
x3cos = xx2cos= xxxx sin2sincos2cos
= xxxx cossin2cos1cos2 22
=2
1.
2
3.2
2
1.1
2
1.2
22
=4
31 = -1
7. A. xtan
x
x
2cos1
2sin
=
1cos21
cossin22
xx= xtan
8. E.
22
223
QP
PQP
xQxP 2sin2cos
=
x
xxxQ
xxP
2
2
cos
1cos
1
22
cossin2
sincos
=
x
xQxP
2cos
1
2tan2tan1
=
2
2
2
1
21
Q
QP
Q
P QP
= 232 2PQPPQ = 323 PPQ
= 223 PQP
=
22
223
QP
PQP
9. D. xtan
x
x
2cos1
2cos1
=
x
x
x
x2
2
2
2
cos2
sin2
1cos21
sin211
= xtan
B. Evaluasi Pemahaman dan Penguasaan
Materi
1. A3cos = AA 2cos= AAAA sin2sincos2cos
= AAxA cossin2cossin21 22
= AAA cossin4cos2
= AA 2sin41cos
A4cos = AA 22cos = AAAA 2sin2sin2cos2cos
= AAxA cossin41cos2sin21 222 = AAAA 2222 cossin81cossin2 = AA
22cossin81
= A2sin212
A3tan = AA 2tan
=
A
AA
an.2an1
2tan2tan
=A
A
A
A
A
A
tan.1
2tan
2
2
tan1
tan2
tan1
tan2
=AA
AA22
3
tan2an1
tantan3
=A
AA2
3
an31
tantan3
A4tan = AA 22tan
=A
A
2an1
2tan22
= 2tan1
tan2tan1
tan4
2
2
1A
AA
A
=
22222
2
tan1
tan4tan1
tan1
tan4
A
AA
A
A
=
AAAA
222
2
tan4tan1
tan1tan4
2. a. A2sin = AAcossin2
=
17
15.
17
8.2 =
289
240
b. A2cos = A2sin21
=
2
7
8.21
=
289
161
c. A2tan =A
A2
an1
tan2
= 61
240
61
225
15
16
1
.2
225
61
1516
2
158
158
3. a. A2sin = AAcossin2
=
25
24.
25
7.2 =
625
336
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b. A2cos = A2sin21
=
2
25
7.21
=
625
527
c. A2tan =A2
tan1
tan2
=
527336
527
576
12
7
1
.2
576527
127
2247
247
4. a. AA 2cos2sin4 = AA 2cos2sin22= A4sin2
b. xx22
cossin4 = xx cossin2 xx cossin2
= x2sin2
c.B
B
3an1
3tan22
= BB 6tan3.2tan
d. 8sin162 A = 1sin28 2 A = A2sin218
= A2cos8
e.0sin
70cos1 = 35cos35sin235sin2
35cos35in35sin211
22
= 35tan
f.2
210cos1 = 105cos
5. a. x2tan =x
x2
an1
tan2
= 4
3
8
9
3
2
1
.22
31
31
b. y2tan =y
y
2tan1
tan2
= 3
41
1
.2
4
32
21
21
c. yx 2tan =yx
yx
2tan.tan1
2tantan
=5
9
3
5
.13
4
3
1
34
31
= 3
d. yx 22tan =yx
yx
2tan.2tan1
2tan2tan
= 34
43
3
4
4
3
.1
6. tan = 180tan= tan
=
tan.tan1
tantan
=
25.41
254
=2201
254
7. 62
tan
t
cos1
cos1
cos1 = cos22 tt
b. cos =2
2
1
1 t
c. tan =
21
2t
a. sin =2
1
2t
8. a.A
sin
2cos1 =
AA
A
AA
A
cossin2
sin2
cossin2
sin211 22
= Atan
b.A
2cos1
2sin
=
1cos21cossin22 A
AA= Atan
c.
2
an1
tan2
=
2
22
cos
sincos
tan2
=
2cos.
cos
sin2
= 2sincossin2
d.
2
2
tan1
tan1
=
2cos
sincos
sincos22
22
9. a.
4tan =
tan.tan1
tantan
4
4
=
an1
tan1
=
sincos
sincos
x
sincos
sincos
=
22
22
sincos
cossin2sincos
=
2cos
2sin1
b.
4tan =
tan.tan1
tantan
4
4
=
an1
tan1
=
sincos
sincos
=
22
22
sincos
cossin2cossin
=
2cos
2sin1
c.
2
2
1
sin2
1
coscos2
=
sin
2
cos1
2
cos1cos2
= sin1cos2 = cossin2cos2
= 2sincos2
d. 2cot =2tan
1=
2
2
tan
1
tan
12
tan2
tan1
=
cot2
1cot2
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e. BBB 2cos2sintan
B
BBBB
cos
2coscos2sinsin =
B
BB
cos
2cos
=B
B
cos
cos
=B
B
cos
cos= 1
f. 1cos21cos2 AA = 1cos4 2 A
= 11cos22 2 A= 12cos2 A
g.CC
C
sincos
2cos
=
C
CC
inos
sincos 22
=
CCCCCC
sincos
sincossincos
= CC cossin
h.1cos
cos2cos
x
xx=
1cos
cos1cos2 2
x
xx
= 1cos
1cos1cos2
x
xx
= 1cos2 x
10. a.
2cos
2sin1 =
22
22
sincos
cossin2cossin
=
sincossincos
sincos2
=
cos1
cos
1
sincos
sincos
=
an1
tan1
b.
2
2sin
2cos
= 2cos1 2
cos1 sin
= sin1
c. 2
2
tan1
tan1
=
2
22
2
22
cos
cossin2sincos
cos
sincos
=2sin1
1
d.A
A
2cos1
2cos1
=
A
A
A
A2
2
2
2
sin
cos
sin211
1cos21
e.xx
sin2sin
2coscos1
=
x
xx
sincossin2
1cos2cos1 2
= xx
xx
cos21sin
cos21cos
= xcot
f.
cossin1
cossin1
=
212
21
21
212
21
21
sin21cossin21
1cos2cossin21
=
21
21
21
21
21
21
cos2sin2sin
cos2sin2cos
= 1
cot
g.
2
1
4tan =
2
24
24
tan.tan1
tantan
=
2
2
2
tan1
tan1
=
sin1
sin1
h. AAA 2coscos22sin 22
= AAAA 2coscos2cossin4 222 = AAA 2cossin2cos2 22 = AAA 222 sin21sin2cos2 = A2cos2
i.CC
CC
ancot
cottan
=
C
C
C
C
tan
tan
tan1
tan1
=
C
C2
2
an1
1tan
=CC
CC
2cos
1
sincos
cossin22
22
= sec2C
j. cosec2B + cot2B =B
B
2sin
2cos
2sin
1
=
BB
B
cossin2
1cos212
= BB
Bcot
sin
cos
11. a. 0sin2sin xx
0sincossin2 xxx
01cos2sin xx
0sin x ;2
1cos x
x = 0 ; 120 ; 180
b. 0cos2cos xx
0cos1cos22 xx
01cos1cos2 xx
2
1cos x ; 1cos x
x = 60 ; 300 ; 180 ; 360 ; 270
c. 05sin32cos xx
05sin3sin212
xx
06sin3sin22 xx
2.2
62.433sin
2
2,1
x
=573
x = arcsin573
; atau
x = arcsin573
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12. a. 8cos2222
= 14cos22222 2
= 4cos422 2
= 4cos222 = 12cos2222 2
= 2cos42 2
= 2cos22
= 1cos222 2 = cos2
b. 8cos2222 = 2cos22
= 2sin2122 = sin2
c. 8cos222sin22
= 2cos2sin22
= 22 sin212sin2 = 2sin212
= 2
cos.2 = 2cos
d. 8cos222cos2 2
= 2cos2cos2
2
= 1cos22cos2 22
= 2cos212 = sin2
C. Evaluasi Kemampuan Analisis
6. 32222 yxyx= 22 2coscos2sinsin AAAA
32coscos2sinsin 22 AAAA
=
AAAA
AAAA
2coscos22sinsin2
2cos2sincossin 2222x
32coscos22sinsin2
2cos2sincossin 2222
AAAA
AAAA
= AAAA 2coscos22sinsin22 x 12coscos22sinsin22 AAAA
= 12cos22cos22 AAAA
= AAA cos22cos4cos4 2
= 2cos2cos4 2 AA
= AA cos21cos222
= AA cos22cos2
= AA 2coscos2 = 2y
8. b. 30tan15tan30tan15tan
= 30tan15tan30tan15tan11530tan= 1
9. a. CBA 2sin2sin2sin
= BABA 1802sin2sin2sin= BABA 2sin2sin2sin= BABABA 2sin2cos2cos2sin2sin2sin
= ABBA 2cos12sin2cos12sin
= ABBA 22 cos2.2sincos2.2sin
= ABBBAA 22 cos2.cossin2cos2.cossin2
= BABABA sincoscossincoscos4 = BABA sincoscos4= BABA 180sincoscos4= CBA sincoscos4
b. CBA 2cos2cos2cos
= BABA 1802cos2cos2cos= BABA 2cos2cos2cos= BABABA 2sin2sin2cos2cos2cos2cos
=
B
BBA
coscossinsin4
2cos2cos12cos
=
BABA
BBA
coscossinsin4
1cos2cos21cos2222
= 1sinsincoscoscoscos4 BABABA= 1coscoscos4 BABA= 1180coscoscos4 BABA
= CBA coscoscos41
c. CBA 2cos2cos2cos
= BABA 1802cos2cos2cos= BABA 2cos2cos2cos= BABABA 2sin2sin2cos2cos2cos2cos = BABBA 2sin2sin2cos2cos12cos
=
BABA
BBA
coscossinsin4
2cossin22cos2
=
BABA
BBA
coscossinsin4
sin21sin2sin21222
= 1sinsincoscossinsin4 BABABA= 1cossinsin4 BABA= 1180cossinsin4 BABA= 1cossinsin4 CBA
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Latihan Kompetensi Siswa 5
A. Evaluasi Pengertian atau Ingatan
1. D.22
1
2
cos1
2sinxx
=2
143
=8
1 = 2
1 =
22
1
2. C.3
1
x
xx
cos1
cos1
2tan
=54
54
11
=9
1 =
3
1
3. D.2
22
2
45sin
2
122sin =
2
45cos1
=2
2121
=4
22
=2
22
4. C. 12
2
45tan3022tan =
45cos1
45cos1
=21
21
21
21
=22
22
= 12
5. B. xcot
2tan
tan
1
2
1
2
xx
=
2
2
2
tan
tan1
2
1x
x
=
x
x
xx
cos1
cos1
cos1cos11
2
1
=
x
x2
cos1
cos2
2
1
=x
x
sin
cos= xcot
7. B. cos
2
2
2
2
tan1
tan1
=
cos1cos1
cos1
cos1
1
1
=
2
cos2 = cos
9. C. -3
cos1
cos1
2sin
=8,01
8,01
=2,0
8,1 = 9 = 3
B. Evaluasi Pemahaman dan Penguasaan
Materi
1. a.2
cos1
2cos
AA
=2
11715
=34
32= 17
17
4
b.A
AA
cos1
cos1
2tan
=1715
1715
1
1
=32
2=
1
c.2
cos1
2sin
AA
=
2
11715
=34
2= 17
17
1
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2. a.2
cos1
2sin
AA
=2
1419
= 41.2
32
= 411
4
b.2
cos1
2cos
AA
=2
1419
= 411
5
c.A
AA
cos1
cos1
2tan
= 419
419
1
1
=50
32 =
5
4
3. a.2
tanA
=
2524
2524
1
1
= 7
b.2
sinA
=2
12524
= 210
7
c.
2
cosA
=
2
12524
=
100
2 = 2
10
1
4. a.A
AA
cos1
cos1
2tan
=
257
257
1
1
=
9
16 =
3
4
b.2
cos1
2cos
AA
=2
1257
=5
3
c.2
cos12
sin AA
=2
1257
=5
4
5. a.2
45tan
1
2
122cot
=
45cos1
45cos1
=21
21
21
21
=2222
= 22
22
=2
222 = 21
g.2
45sin2122sin =
245cos1
=2
2121
=4
22
=2
22
h.2
45cos
2
122cos =
2
22
6. a. AA cotseccos =A
A
A sin
cos
sin
1
=A
A
sin
cos1
=
22
2
2
cossin2
sin211AA
A
=2
2
cos
sinA
A
=2
tanA
b. 1cos2
tan AA
=
2
2
cos
cos1sinA
A A
=
2
2
2
2
cos
1cos21sinA
AA
=2
2
2
2
cos
cossin2
A
AA
=2
cos2
sin2AA
= sinA
c.
2
2sin2cos
xx
= cos2sin22cos2sin
22 xxxx
= xsin1
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d. BB
cos2
cos2 2 = 1cos12
cos2 2
B
B
= 1coscos BB
= 1
e.2
cos
1
2sec
x
x =
2cos1
1
=
cos1
2
f. cotseccos =
sin
cos
sin
1
=
sin
cos1
=
22
2
2
cossin2
1cos21
=2
2
sin
cos
=2
cot
7.
22
sin
sin
A
DA
n
=
2cos1
2
cos1
A
DA
=
A
DA
cos1
cos1
8.
cos1
sin1
=
1cos21cossin21
2
2
22
=2
2
2
2cos
sin
cos2
1
=2
tancos
cossin
2
1
2
2
2
2
2
2
=2
tan12
tan2
1 2
=
2tan21
2tan
21 2
=
2
12
tan2
1
9. a.
sin2
coscos2
sin2
1sin
=13
5
2
12524
+13
12
2
12524
= 2130
5+ 2
130
84
= 213089
b.2
sincos2
cossin2
1sin
=2
1.
25
7 135
+2
1.
25
24 135
= 1326
6.
25
7+ 13
26
4.
25
24
= 13650
138
c.
sin2
sincos2
cos2
1cos
=13
5
2
12524
+13
12
2
12524
=13
5.2
10
7+
13
12.2
10
1
= 2130
47
d.
2
1cos =
13
5
2
1 2524
-13
12
2
1 2524
=13
5.2
10
7-
13
12.2
10
1
= 2130
23
e.
2
1tan =
2tan.tan1
2tantan
=
135
135
135
13
5
1
1
247
1
1
247
.1
=
58
49
.164
247
64
247
f.
2
1tan =
512
1
1
5
12
1
1
..12524
2524
2524
2524
=
23
89
.15
1271
512
71
g.
2
1tan =
512
1
1
512
1
1
..125
24
2524
2524
2524
=
47
79
.15
1271
512
71
h.
2
1cos =
2
1.
25
24 135
+2
1.
25
7 135
= 1326
6.
25
24+ 13
26
4.
25
7
= 13650
172
10. a. 15sin21 2 = 30cos = 0,866
b. 2
122sin
2
122cos
22= 45cos = 0,7071
c. 15cos.15sin =21.
2130sin
21 = 0,25
d.
212
21
22tan1
22tan2= 45tan = 1
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C. Evaluasi Kemampuan Analisis
1. a. CBA sinsinsin
= BABA 180sinsinsin= BABA sinsinsin= BABABA sincoscossinsinsin
= ABBA cos1sincos1sin
=2
cos2.2
cos2
sin22 BAA
+2
cos2.2
cos2
sin22 ABB
=
2sin
2cos
2cos
2sin
2cos
2cos4
BABABA
=
22sin
2cos
2cos4
BABA
=
BA
BA180
2
1cos
2cos
2cos4
=
2
cos
2
cos
2
cos4CBA
b. CBA sinsinsin
= BABA 180sinsinsin= BABA sinsinsin= BABABA sincoscossinsinsin = ABBA cos1sincos1sin
=2
sin2.2
cos2
sin22 BAA
+2
sin2.2
cos2
sin22 ABB
=
2cos
2sin
2cos
2sin
2sin
2sin4
BAABBA
=
22sin2sin2sin4BABA
=
BA
BA180
2
1cos
2sin
2sin4
= cos2
sin2
sin4CBA
3. a.
b
aarccos
2
1
4tan
=
24tan
=2
2
tan1
tan1
=
b
ab
a
b
ab
a
1
1
1
1
1
1
b
aarccos
2
1
4tan
=
b
ab
a
b
ab
a
1
1
1
1
1
1
b
aarccos
2
1
4tan
+
b
aarccos
2
1
4tan
=
ba
ba
ba
b
a
1
1
1
1
1
1
+
ba
ba
ba
b
a
1
1
1
1
1
1
= a
b
ba
b
ab
a
ba
b
a
2
2
4
1
22
1
1
1
1
Latihan Kompetensi Siswa 6
A. Evaluasi Pengertian atau Ingatan
1. A. 13
15cos45sin4 = 30sin60sin2
=
2
13
2
12 = 31
2. A.23
15cos75sin = 60sin90sin2
1
=
3
2
11
2
1
=
32
1
3. E.1
15cos75cos2 = 60cos90cos
=1
0 =2
1
4. A.2
23
75sin105sin = 30cos180cos
=
3
211
=2
32
5. D.12
2
137cos
2
17sin = 30sin45sin
2
1
=
2
12
2
1
2
1
=4
12
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8. D. 2cos
45cos45cos2 = 2cos90cos = 2cos
9. A. 2sin
2sin
2cos2 = 2sinsin
= 2sin0
= 2sin
B. Evaluasi Pemahaman dan PenguasaanMateri
1. a. cos4sin = 3sin5sin2
1
b. BABA cossin2 = BA 2sin2sin
c. BABA 2
1sin
2
1cos = BA sinsin
d. 90sin90cos2 = 2sin180sin = 2sin
e. 85cos15sin2 = 70sin100sin
= 70sin100sin
f. 2
1sin
2
3cos2 = sin2sin
= 0
2. a. baba coscos2 = ba 2cos2cos
b. baba 2
1cos
2
1cos2 = ba coscos
c. baba 2sin2sin = ba 2cos4cos2
1
d. cbacba sinsin2 = cba 2cos2cos
e. 4
1cos
2
1cos =
4
1cos
4
3cos
2
1
f. 20sin200sin2 = 180cos220cos
3. a. 110cos70cos2 = 40cos180cos = 40cos1
b. 50sin40sin2 = 10cos90cos = 10cos0 = 10cos
c. 60cos80sin2 = 20sin140sin
d. 50sin110cos2 = 60sin160sin
= 32
1160sin
4. a. BAsinsin = BABA sinsin2
1
b. xx sin5cos3
= xx 4sin6sin3
c. xx2
3sin
2
5cos5 = xx sin4sin
2
5
d. yxyx cos53cos =
yxyx 42cos64cos2
1
e. CBACBA sincos =
CBA 2sin2sin2
1
f. AA 3cos5sin = AA 2sin8sin2
1
g. 40cos200cos = 160cos240cos2
1
h.
4cos
4sin10
=
2sin2sin5
i. BABA 2
1sin
1sin
2
1= BA coscos1
j.
BABA 3
2
13sin
2
7cos =
BABA 23sin410sin1
k. AA 8cos7cos3 = AA cos15cos2
3
l. AA4cossin8
= AA3sin5sin4
5. a. 15cos75sin = 60sin90sin2
1
=
3
2
11
2
1
=4
32
b. 15sin75cos = 60sin90sin2
1
=
3
2
11
2
1
=4
32
c. 15cos75cos = 60cos90cos2
1
=
2
10
2
1
=1
d. 15sin75sin = 60cos90cos2
1
=
210
21 =
41
e.
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7. a. 3cos2cos5cos24sin3sin2 =
3cos3cos7coscos7cos = cos
b.
AA
AAAA
2
7cos
2
3sin2
2
3cos
2
5sin2
2
3cos
2
1sin2
=
AAAAAA
2sin
5sinsin4sinsin2sin
= AA 5sin4sin
9. a. 4sin12sin2sin6sinsin3sin
32sin96sin16sin48sin8sin24sin
=
64cos128cos32cos64cos
16cos32cos8cos16cos
4cos8cos2cos4cos
2
1
= 2cos128cos21
=
2
2128sin
2
2128sin
= 63sin65sin
b. 4cos12cos2cos6coscos3cos 8cos24cos
=
16cos32cos8cos
16cos4cos8cos2cos4cos
= 32cos2cos
= 2232sin
2232sin
= 15sin17sin
Latihan Kompetensi Siswa 7
A. Evaluasi Pengertian atau Ingatan
1. B. 1
20sin0sin
70cos20cos=
25sin5cos2
25sin45sin2= 1
4. E.2
1
15cos105cos = 45cos.60cos2
=
2
2
1
.2
12
= 22
1=
2
1
6. B. BA tan
AB
AB
2sin2sin
2cos2cos
=
BABA
BABA
cossin2
sinsin2
= BA tan
7. E. cot
3coscos
3sinsin
=
sin2sin2
cos2sin2= cot
8. E. x2cot
x
xx
3coscos
sin3sin
=
xx
xx
in2in
sin2cos2= x2cot
9. A.
2tan
coscos
sinsin
=
22
22
coscos2
cossin2
=
2tan
10. D. xtan
xx
xx
5coscos
5sin7sin
=
xx
xx
cos6os2
sin6cos2= xtan
15. D. Atan
AA
2cossin1
2cos2sin1
=
1cos2cossin21
sin21cossin212
2
AAA
AAA
=AA
AAA2
2
cos2cossin2
sin2cossin2
= AAA
AAA
cos2sin2cos
sin2cos2sin
= Atan
B. Evaluasi Pemahaman dan Penguasaan
Materi
1. a. 3sinsin = cos2sin2
b. 2coscos =
2
cos
2
3cos2
c. 3coscos = sin2sin2
d. 2sinsin =
2cos
2
3cos2
e. AA 2cos4cos = AAsin3sin2
f. yxyx coscos = yx coscos2g. BABA 62sin24sin =
BABA 2sin43cos2 h. qpqp sin53sin =
qpqp 3cos22sin2 i.
yxyx 34cos2cos =
yxyx 2cos3cos2 j. BABA 2cos2cos = BA 2sinsin2
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2. a. 50sin40sin = 5cos45sin2 = 5cos2
b. 10cos70cos = 30cos40cos2 = 40cos3
c. 40cos80cos = 20cos60cos2 = 20cos
d. 10sin70sin = 30sin40cos2 = 40cos
e. 35sin55sin = 10cos45sin2 = 10cos2
f. 52cos68cos = 8cos60cos2 = 8cosg. 35cos95cos = 30cos65cos2 =
65cos3
h. 30cos70cos = 20sin50sin2
i. 40sin80sin = 20sin60cos2 = 20sin
4. a. 15sin105sin = 45cos60sin2
= 22
1.3
2
1.2
= 6
2
1
b. 165cos465cos = 150sin315sin2
=1
.22
1.2
= 22
1
c. 15cos105cos = 45cos60cos2
= 22
1.
2
1.2
= 22
1
f. 15sin75sin = 30sin45cos2
=2
1.2
2
1.2
= 22
1
g.
15sin70sin
15cos70cos=
5,27sin5,42cos2
5,27sin5,42sin2
= 5,42tan
h.
15sin75sin
15cos75cos=
30sin45cos2
30cos45cos2
= 30cot= 3
i. 15sin5sin
15cos75cos=
30cos5sin2
30sin45sin2
= 33
1
5. a.10
3sin
5sin
=
20sin
4cos2
=
20
sin2
b.12
11sin
12sin
=
24
10cos
2sin2
d.
2
3sin2
3sin =
2sin
6cos2
= 2sin.32
1.2
= 2sin3
e.10
3cos
5cos
=
10cos
2cos2
= 0
g.
12cos
12
5cos =
2
3cos
2cos2
7. a.
3sin7in
3cos7cos
= cos5sin2
2cos5cos2
= 5cot
b.
coscos
sin5sin
=
2coscos2
2cos3sin2
= 3tan
c.
3sin5sin
3cos5cos
=
sincos2
cos4cos2
= cot
d.
sin6sin
4cos6cos
=
cos5sin2
sin5sin2
= tan
e.
6os8cos6sin8sin
=
cos7cos2sin7cos2
= tan
f.
os3cos
sin3sin
=
sin2sin2
sin2cos2
= 2cot
g.
sinsin
coscos
=
22
22
sincos2
sinsin2
=
2
tan
h.
2cos2cos
2sin2sin
=
coscos2
sincos2
= tan
j.ts
ts
coscos
sinsin
=
22
22
coscos2
cossin2
tsts
tsts
=
2tan
ts
8. a. 20sin80sin = 30sin50cos2
= 50cos
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b. 25sin65sin = 20cos45sin2
= .22
1.2 20cos
= 2 20cos
d.
12
sin
12
5sin
=
6
cossin2
= 32
1.2
2
1.2
= 62
1
e.
33cos3cos
33sin3sin=
15cos18cos2
15cos18sin2
= 18tan
f. 10cos50cos
50sin10sin=
20sin30sin2
20sin30cos2
= 3
g. 40cos20cos
20sin40sin = 10sin30sin210sin30cos2
= 3
=
10cos50cos
50sin10sin
h.
20sin70sin
20cos70cos=
25cos5sin
25cos45cos2= 1
9. a. CBA 2sin2sin2sin
= BABA 1802sin2sin2sin= BABA 2sin2sin2sin
= BABABA 2sin2cos2cos2sin2sin2sin = ABBA 2cos12sin2cos12sin = BABABA cossinsincossinsin4 = BABA sinsinsin4= BABA 180sinsinsin4= CBA sinsinsin4
b. CBA coscoscos
= BABA 180coscoscos= BABA coscoscos= BABABA sinsincoscoscoscos = BABBA sinsincoscos1cos
=
2
sin21 2A
2sin2 2
B+
2
sin21 2B
+
2cos
2cossin
2sin4
BABA
=2
sin2
sin2
sin41CBA
c. CBA sinsinsin
= BABA 180sinsinsin
= BABA sinsinsin
= BABABA sincoscossinsinsin
= ABBA cos1sincos1sin
=2
cos2.2
cos2
sin2 2BAA
+2
cos2.2
cos2
sin2 2ABB
=
2sin
2cos
2cos
2sin
2cos
2cos4
BABABA
=2
cos2
cos2
cos4CBA
d. CBA sinsinsin = BABA 180sinsinsin= BABA sinsinsin
= BABABA sincoscossinsinsin = ABBA cos1sincos1sin
=2
sin2.2
cos2
sin2 2BAA
+2
sin2.cos2
sin2 2ABB
=2
cossin2
sin4CBA
C. Evaluasi Kemampuan Analisis
1. a.
2cos
A+
2cos
B+
2cos
C
=
2cos
A+
2cos
B+
2
180cos
BA
=
2cos
A+
2cos
B+
2sin
BA
=
2cos
A+
2cos
B+
2sin
2cos
2cos
2sin
BABA
=
2cos
A
2sin1
B+
2cos
B
2sin1
A
=
4cos4
A
4cos
B
4cos
C
4. a.C
CBA
sinsinsin
sinsinsin
=
222
222
cossinsin4
coscoscos4
CBA
CBA
=
2
cotA
2
cotB
b.CA
CBA
sinsinsin
2sin2sin2sin
=
222coscoscos4
sinsinsin4
CBA
CBA
=222
222222
coscoscos
cossin2.cossin2.cossin2
CBA
CCBBAA
=2
sin2
sin2
sin8CBA
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Kunci Penyelesaian Matematika SMA Jl.2A- Sukino Bab 3 | page 77
Ujian Kompetensi Akhir Bab 3
A. Pilihan Ganda
1. A.p
q1
qBABABA sincoscossinsin
qpBA sincos
p
qp
BA
BABA
cossin
sincostancot =
p
q1
2. E. 22
1
12cos
12
7cos
= coscos2
= .2
1.2 2
2
1= 2
2
1
3. E.65
63
sin = sincoscossin
=5
4.
13
12
5
3.
13
5
=65
63
4. B. m-n
sin = sincoscossin = n sincos = m-n
5. A. 0
BA sin = BABA sincoscossin = 30sin =2
1
BAsincos =4
1
BA sin =
4
1
4
1= 0
6. B. sin4cos2
4sin 4sin = sin4cos2
7. E. 6cos
3cos4 3sin 4 =
3sin3cos 22 3sin3cos 22 = 6cos
8. A. 32
660tan840tan =
300360tan120360.2tan = 300tan120tan
= 120180tan120tan = 120tan120tan
= 120tan2 = 60180tan2 = 60tan2 = 32
9. D. 3152
1
yxcos = yxyx sinsincoscos = 51
ycoscos = 51
- 34
1
yxyxyx
coscossinsintantan =
35341
41
4
1
= 3152
1
10. B. 12
2
135tan5,67tan =
135cos1
135cos1
=21
21
21
21
=22
22
= 22
22
= 12
11. E.2
2
1
1
p
p
22 sincos2cos
= 22 coscos p
= 22 cos1
p
= 2
2
1
11
pp
=
2
2
1
1
p
p
dimana :
2
2
2
cos
sinp
2
2
2
cos
cos1p
2
21
cos
1p
2
21
cos
1p
2
2
1
1cos
p
12. E. 22 11 pqqp
sin = sincoscossin
= qpqp .11 22
13. C. 12
x
A2
1cos =
x
x
2
1A
1cos
Asin 12 x
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14. B. 2
50cos0os
10cos=
10cos90cos10cos
21
= 2
15. A. 152
1
x
xx 2an1
tan22tan = 2
xx 2tan22tan2
02tan2tan2 2 xx
01tantan 2 xx
1.2
1.1.411tan
x =
2
51
1tanx = 51
2
1 ;
2tanx =
2
15
16. A.
2
cosA
2sin
CB=
2
180sin
A
=2
sin90cos2
cos90sinAA
=2
cosA
17. B.
2sin2
A
2cos
CB
CB coscos = CBCB coscos2
=
2cos
2
180cos2
CBA
=
2cos
290cos2
CBA
=2
sin2A
2cos
CB
24. D. 29
4
BA 32sin = BABA 3sin2cos3cos2sin
= 3
1
BA 32cos = BABA 3sin2sin3cos2cos
= 23
2
BA 32sin BA 32cos =
BA 6sin4sin2
1 = 2
2
BA 6sin4sin = 29
4
25. A. 32
1
75cos4 75sin 4 = 150cos = 32
1
26. D. 2cos22
22 yx =
cos3cos2cos3cos
sin3sin2sin3sin
22
22
= 2cos22
31. A.22
13
k
k
20sin10sin
35cos25cosk =
10cos30cos
10cos60cos
2
1
21
10cos2
110cos3
2
1
k
32
1
2
1110cos kk
1
3110cos 2
1
k
k
=22
13
k
33. E. 62
15os
1
75cos
1=
75cos15cos
75cos15cos
= 60cos90cos
30cos45cos2
2
1
=21
21
21
21
.
3.2.2
= 62
36. A.
tantan1
tantan
cos
sin=
coscos1
coscos1
sinsincoscos
sincoscossin
=
tantan1
tantan
38. D. Asin2
1
28sin 2 A -
28sin2 A
=
28
sin28
sinAA
.
28
sin28
sinAA
=
2cos
8sin2
A
2sin
8cos2
A
= Asin.sin
= Asin2
1
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39. C.
15tan1
15tan15tan32
3
= 1530tan45tan
=
15tan30an1
15tan30tan
=
15tan.1
15tan
15tan115tan2
15tan1
15tan2
2
2
=
15an31
15tan15tan32
3
40. A. AA 4cos8
1cos
2
13
A4
sin = 22sin A
=
2
2
cos1
A
=4
coscos21 2 AA
=4
cos212
14cos AA
= AA 4cos8
1cos
2
1
8
3
B. Bentuk Uraian
1. a. ts sin = tsts sincoscossin
= 21
.5
42
2
1.
5
3
= 210
1
b. ts cos = tsts sinsincoscos
= 22
1.
5
32
2
1.
5
4
= 210
1
2. a.
h
xfhxf=
xhx sinsin
=xxx sinsinhcoscoshsin
=
hx
hx
sinhcos
1coshsin
b. xghxg
= xhx coscos
=xxx cossinhsincoshcos
=
hxhxsinh
sin1cosh
cos
c. xThxT
= xhx tantan
=h
xx
x tantanhtan1tanhtan
= tanh.tan1
tanhtantantanhtan2
xh
xxx
= tanh.tan1tan1tanh
2
xhx
=anhan1
sectanh2
x
x
3. a. BA cot =BA
BA
BA
BA
tantan1
tantan1
tantan
tantan1
=AB
BA
cotcot
1cotcot
b. BA cot =BA
BA
tanan
tantan1
=AB
BAcotot
1cotcot
4.
24tan
=
24
24
tantan1
tantan
=
2
2
tan1
tan1
x
x
x
x
x
x
x
x
1
2
1
2
1
2
1
2
1
11
1
11
=x
x
x
x
x
111
1
1
1
1
5. a.
1
1
1
1
sin
sin
sin
sin
BA
BA
BA
BA
c
c=
B
A
BA
BA
tan
tan
sincos2
cossin2
Atan = Bc
ctan
1
1
6. a.
2sin2tan
2sin2tan
y
x
=
12cos
12sin
12cos
12sin
=
2cos1
2cos1
= 2tan
b. 222 2sin2tan2sin2tan = 22sin2tan4
= 2sin2tan16 22
=
2sin.
2cos
2sin16 2
2
2
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=
2sin
2cos
2cos116 2
2
2
=
2sin12cos
116 2
2
= 2sin2tan16 22 = 2sin2tan16 2sin2tan = xy16
9. mx
xx
2cos1
2cos1tan
xmmx 2cos2cos1 22
c.2
2
1
12cos
m
mx
a.
22
2222
1
2
1
112sin
mmmx
b. xxx 2sin3sin= xxxx sin2coscos2sin
=22
2
22
1.
1
1
1
1.
1
2
m
m
m
m
mm
m
=
323
1
3
m
mm
d. x3cos = 22
2
1.
1
1
m
m
m
m
- 22
1
1.
1
2
mm
m
=
322
1
31
m
m
10. a. x5sin = xx 32sin = xxxx 3sin2cos3cos2sin
= xxxxx sin2sincos2cos2sin2
xxxxx sin2coscos2cos2sin2
= xxxxx cos2cos2sin24cossin
b. x5cos =
xx 32cos
= xxxx 3sin2sin3cos2cos
= xxxxx sin2sin2coscos2cos2
xxxxx sin2cos2sincos2sin2
= xxxxx 2cos2sinsin24coscos