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• Trigonometri berasal dari bahasa Yunani trigonon = tiga sudut dan metro = mengukur. Jadi Trigonometri adalah cabang ilmu matematika yang berhadapan dengan sudut segitiga dan trigonomertik seperti sinus, cosinus, dan tangen.Maka kita akan membahas tentang sinus, cosinus, dan tangen yang biasa disebut sin, cos, tan

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• SINUS ALPHA

COSINUS ALPHA

• COSINUS ALPHA

• TANGEN ALPHA

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Dari Persamaan diatas dapat disimpulkan bahwa :

Example:Jika c = 120 cm dan alpha = 30 derajat, maka panjang AC sama dengan ?

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• Dalam Trigonometri ada sudut sudut istimewa yaitu sudut (derajat) 0, 30, 45, 60, 90Tabel sin, cos, dan tan sudut istimewa

Data tabel diatas diambil/didapat dari segitiga dibawah ini :

Jika c = 120 cm dan alpha = 30 derajat, maka panjang AC sama dengan ?

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GEOMETRY Geometry is the measurement of dimensions, areas,and volumes of geometric shapes, and is quite useful in aviation maintenance. In fact, it is geometry that allows you to calculate the displacement of a cylinder. determine the volume of a fuel tank, and calculate the surface area of a wing. On the other hand. trigonometry allows you to determine unknown lengths and angles of a triangle. ln addition to aiding you when fabricating sheet metal, trigonometry plays a large part in the theory of alternating current .THE RECTANGLEAs you know, a rectangle is a four sided planed. It is distinguished by having opposite sides of equal length, and four angles each equal to 90o degrees. The formula for the area of a rectangle is:Area= Length x Width or A = L x W

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• Before the mathematical operation can be carried out, both measurements must reflect the same unit of measure.

• Ex: Given a sheet of aluminum that is 48 inches wide by 12 feet long. Calculate the area of the Aluminum sheet. (you must convert either the width to feet or the length to inches).

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SQUAREA square is a symmetrical plane in which all four sides are equal length. The formula used for a rectangle is used to find the area of a square. However since all sides of a square are of equal length, the formula is sometimes expressed as the square of the sides :

A = S2

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THE TRIANGLEThe triangle is a three-sided figure consisting ofthree angles whose combined measurement equals180 degrees. Three basic types of triangles youshould be familiar with are: the scalene triangle,which consists of three unequal angles and sides,the equilateral triangle, which has equal sides andequal angles. and the isosceles triangle, which hastwo equal angles.

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Triangles are further classified by the measurement of one angle. For example, a right triangle is one that has one angle measuring 90 degrees. ln an obtuse triangle. one angle is greater than 90 degrees, while in an acute triangle all angles are less than 90 degrees.There are several terms associated with triangles. For instance. the base of a triangle is the side the triangle rests or stands on. Depending on a triangle’s orientation, any side may be the base. The vertex is a common endpoint, or the point where the sides of the triangle meet. The altitude of a triangle is the height of the vertex above the base.

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If a triangle is set in a rectangle and the triangle’s base and height are equal to two of the rectangle’s sides, the area of the triangle is exactly one-half that of the rectangle. Therefore, the formula for calculating the area of a triangle is one-half the base times the height, or 1/2 b.h. Find the area of a triangle whose base is 6 inches and height is 15 inches. Step 1: Insert given values into the formula.

A = 1/2 6 X 15Step 2: Perform multiplication.

A : 45 square inches

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THE PARALLELOGRAM The parallelogram, like the rectangle, has opposite

sides that are parallel and equal in length. However, the corner angles of a parallelogram are some measurement other than 90 degrees. The area of a parallelogram is calculated by multiplying the length by the height (A = l x h). The height is measured perpendicular to the length, similar to the way the altitude of a triangle is determined.

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THE TRAPEZOIDA trapezoid is a four-sided figure that has one set of parallel sides. If you lay two trapezoids side by side so the top and bottom sides form straight lines, a parallelogram is formed with a base that is equal to the combined length of the trapezoid’s parallel sides. As discussed earlier, the area of a parallelogram is found by multiplying the length, which in this case equals the sum of the parallel sides, by the height. However, because the area of a single trapezoid is one-half that of the parallelogram, the trapezoid’s area is equal to one-half the product of the base times the height. This is expressed with the formula:

Area = ½(base1 + base 2) x Height

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THE CIRCLEA circle is a closed figure bounded by a single curved line. Every point on the line forming a circle is an equal distance from the center. The distance from the center to the line forming the circle is called the radius, and the distance around the circleis known as the circumference. The diameter of a circle is represented by a line that touches two points on the outside of the circle and passes through the circle’s center. The circumference has a definite relationship with the diameter. This relationship is represented by the Greek letter pi ( ), and is equal to 3.1416.

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• The ratio of the circumference to the diameter of a circle is always pi. Regardless of the size of the circle, pi is a constant. The circumference of a circle is found by multiplying pi times the diameter, and the area is calculated by multiplying pi times the square of the radius. For example, if a circle has a diameter of 10 inches, determine the circumference and area.

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COMPUTING VOLUME

Solids are objects with three dimensions: length, width, and height. Having the ability to calculate volume enables you to determine the capacity of a fuel tank or reservoir. figure the capacity of a cargo area, or calculate the displacement of a cylinder. Volumes are calculated in cubic units, such as cubic inches, cubic feet. and cubic centimeters. However, volumes are easily converted to useful terms such as gallons. For example, to convert cubic inches to gallons, divide the total number of cubic inches by 231.If converting cubic feet to gallons, remember that 1 cubic foot holds 7.5 gallons

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VOLUME OF A RECTANGLEThe volume of a rectangular solid is found by multiplying the dimensions of length, width, and height. When calculating volume, it is important that all measurements be in like terms. The formula for determining the volume of a rectangular solid is:

V = L x W x HWhere:V = volumeL : lengthW : widthH = height

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• Ex: Calculate the volume of a rectangle when its dimension is as follows:

Length : 24 inchesWidth : 18 inchesHeight : 12 inches

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VOLUME OF A CUBE

A cube is a solid with equal sides. Since all dimensions of a cube are identical, its area is calculated by multiplying one dimension by itself three times.The formula is:

Volume = S3

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VOLUME OF A CYLINDERA cylinder is a solid with circular ends and parallel sides. Its volume is found by multiplying the area of one end by the cylinder’s height. The formula is expressed as:

Volume = r2 H

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As a technician, you can use this formula to calculate piston displacement. Piston displacement is defined as the volume of air displaced by a piston as it moves from bottom center to top center. For example, one cylinder of a four-cylinder aircraft engine has a bore, or diameter, of four inches and the piston has a stroke of six inches. Stroke is defined as the distance the head of a piston travels from bottom center to top center. What is the total cylinder displacement??

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VOLUME OF A SPHERE

A sphere is any round body having a surface on which all points are an equal distance from the center of the sphere. A sphere has the greatest volume for its surface area, and is used in aircraft systems for hydraulic accumulators and liquid oxygenconverters.

VOLUME : 4/3 r3

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CONEA solid with a circle as a base and with sides that

gradually taper to a point is called a cone. the formula for the volume of a cone is :

1 2.3 .V Hr

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THE METRIC SYSTEMThe metric system is the dominant language of measurement in use today. However, in the United States, the customary units of measurement include the English units of inches, feet, ounces, and pounds. While these units have proved functional for many years, they are cumbersome to convert. The meter as a standard was developed in France and adopted by the National Assembly of France in the late 18th century. The United States government legalized the use of the metric system in 1866, but it was not until the Metric Bill of 1975 that its use became common. We are still in a time of slow conversion to the metric system and in many cases both Metric and English units appear together on packaging, speedometers, and thermometers. The metric system is built on decimal units. Each basic unit is divided or multiplied by ten as many times as necessary to get a convenient size. Each of the multiples has a definite prefix, symbol, and name. As a technician, you must be familiar with each of them.

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There are six base units in the metric system. The unit of length is called the meter, and is approximately 39 inches. The metric unit of mass, or weight, is the gram. The unit of time is the second. The unit of electrical current is the ampere. The unit of temperature is the degree Celsius, formerly called degree Centigrade. The unit of luminous intensity is the candela. All other units of measurement in the International System of Units, which is now called SI, are derived from these six. Conversion from English to Metric systems is accomplished in a variety of ways. Many hand-held electronic calculators now have specific function keys for making these conversions.

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All of the metric units follow a consistent naming scheme, which consist of attaching a prefix to the unit. For example, since kilo stands for 1,000, one kilometer equals 1,000 meters. Centimeter is prefix for hundredth, so one meter equals one hundred centimeters. Millimeter is the prefix for one thousandths and one gram equals one thousand milligrams.