Fungsi dan Grafik Fungsi Trigonometri
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FUNGSI & GRAFIK FUNGSI FUNGSI & GRAFIK FUNGSI TRIGONOMETRI TRIGONOMETRI 1 FUNGSI &GRAFIK FUNGSI TRIGONOMETRI Oleh: Aururia Begi Wiwiet Rambang ACA 111 0064 1
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Transcript of Fungsi dan Grafik Fungsi Trigonometri
FUNGSI & GRAFIK FUNGSIFUNGSI & GRAFIK FUNGSI TRIGONOMETRITRIGONOMETRI
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FUNGSI &GRAFIK FUNGSITRIGONOMETRI
Oleh:Aururia Begi Wiwiet Rambang
ACA 111 0064
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ATURAN SINUSATURAN SINUS
SinCc
SinBb
SinAa ==
Bukti :Bukti :
SinΑb
CD =
aSinBCD =b.SinACD =
SinBa
CD =
aSinBbSinA =
SinB
b
SinA
a =
CONTOH SOAL :CONTOH SOAL :
Pada segitiga ABC, diketahui
c = 6, sudut B = 600 dan sudut C = 450.
Tentukan panjang b !
0
PENYELESAIAN :PENYELESAIAN :
2
6
3
45
6
60
21
21
00
=
=
=
bSinSin
bSinC
c
SinB
b
632
66
2
2
2
36
2
63
21
21
==
•=
×=
b
b
b
ATURAN KOSINUSATURAN KOSINUS
2bcCosA2c2b2a −+=
2acCosB2c2a2b −+=
2abCosC2b2a2c −+=
CONTOH SOAL :CONTOH SOAL :
Pada segitiga ABC, diketahui
a = 6, b = 4 dan sudut C = 1200 Tentukan panjang c
PENYELESAIAN :PENYELESAIAN :c2 = a2 + b2 – 2.a.b.cos Cc2 = (6)2 + (4)2 – 2.(6).(4).cos 1200
c2 = 36 + 16 – 2.(6).(4).( – ½ )c2 = 52 + 24 c2 = 76 c =√76 = 2√19
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Berhenti sejenak…
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b. Membuat Grafik Fungsi Trigonometri
a. Grafik y = sin xo , 00 ≤ X ≤ 3600
x 0 30 90 150 180 210 270 330 360
y 0 ½ 1 ½ 0 -1/2 -1 -1/2 0
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1
0
-1
90 0 180 0
270 0
360 0
Y = sin xy
x
Sine graphsSine graphs
y = sin(x)
y = sin(3x)
y = 3sin(x)
y = sin(x – 3)
y = sin(x) + 3
y = 3sin(3x-9)+3y = sin(x)
y = sin(x/3)
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b. Grafik y = Cos xo ; 00 ≤ X ≤ 3600
x 0 60 90 120 180 240 270 300 360 y 1 1/2 0 1/2 -1 - 1/2 -1 1/2 1
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1
0
-1
90 0180 0
270 0
360 0
Y = Cos x
Graphs of cosineGraphs of cosine
y = cos(x)
y = cos(3x)
y = cos(x – 3)
y = 3cos(x)y = cos(x) + 3
y = 3cos(3x – 9) + 3y = cos(x)
y = cos(x/3)
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c. Grafik y = tg xo
x 0 45 90 135 180 225 270 315 360
y 0 1 ∞ -1 0 1 ∞ 1 0
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1
0
-190 0 180 0
270 0
360 0
Y = Tg x
45 0
315 0135 0
225 0
Graphs of tangent and Graphs of tangent and cotangentcotangent
y = tan(x)Vertical asymptotes at
y = cot(x)Verrical asymptotes at .πnx =.
2ππnx +=
Graphs of secant and cosecantGraphs of secant and cosecant
y = sec(x)Vertical asymptotes atRange: (–∞, –1] U [1, ∞) y = cos(x)
y = csc(x)Vertical asymptotes atRange: (–∞, –1] U [1, ∞) y = sin(x)
.2
ππnx += .πnx =
Ηαλ.: 25
ΒΑΡΙΣΑΝ ∆ΑΝ ∆ΕΡΕΤ
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