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Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023

Chapter 3

Mathematics in Aviation Maintenance

Figure 3-27. Cylinder displacement.
Figure 3-27. Cylinder displacement.

given as:

Formula: Surface area = 4 × π × radius2 = 4 × π × r2

Cone

The formula for the surface area of a right circular cone [Figure 3-29] is given as:

Formula: Surface area = π × radius × [radius + √(radius2 + height2)] ; = π × r × [r + √(r2 + h2)]

Figure 3-30 summarizes the formulas for computing the volume and surface area of three-dimensional solids.

Trigonometric Functions

Trigonometry is the study of the relationship between the angles and sides of a triangle. The word trigonometry comes from the Greek trigonon, which means three angles, and metro, which means measure.

Right Triangle, Sides, and Angles

In Figure 3-31, notice that each angle is labeled with a capital letter. Across from each angle is a corresponding side, each labeled with a lower case letter. This triangle is a right triangle because angle C is a 90° angle. Side “a” is “c” is always across from the right angle and is referred to as the “hypotenuse.”

Figure 3-28. Sphere.
Figure 3-28. Sphere.

Sine, Cosine, and Tangent

The three primary trigonometric functions and their abbreviations are: sine (sin), cosine (cos), and tangent (tan). These three functions can be found on most scientific calculators. The three trigonometric functions are actually ratios comparing two of the sides of the triangle as follows:

Formula: opposite side (side a) ; Sine (sin) of angle A = ; hypotenuse (side c) ; adjacent side (side b) ; Cosine (cos) of angle A = ; hypotenuse (side c) ; opposite side (side a) ; Tangent (tan) of angle A = ; adjacent side (side b)

Example: Find the sine of a 30° angle.

Calculator Method:

Using a calculator, select the “sin” feature, enter the number

Formula: 30, and press “enter.” The calculator should display the ; answer as 0.5. This means that when angle A equals 30°, then ; the ratio of the opposite side (a) to the hypotenuse (c) equals ; 0.5 to 1, so the hypotenuse is twice as long as the opposite ; side for a 30° angle. Therefore, sin 30° = 0.5.

Trigonometry Table Method: