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28 Part I: Technical Mathematics
Pythagorean Theorem
Part I.D
The sides of a right triangle are related according to the Pythagorean theorem, which
states that the sum of the squares of the lengths of the sides of a right triangle
equals the length of the hy potenuse squared:
The relationship can also be written as
a 2 + b 2 + c 2
2 2
a + b = c.
Using the theorem, the length of a third side can be found if the lengths of two sides
are known. For example, if side a = 3cm and b = 4 cm, the length of hy potenuse c
can be found:
TRIGONOMETRIC FUNCTIONS
2 2
3 + 4 = c
25 = c
5 = c
There are six main trigonometric functions, which express the ratios of the sides
of a right triangle. These functions are: sine (sin), cosine (cos), tangent (tan),
cotangent (cot), secant (sec), and cosecant (csc). These functions and their calculations
are illustrated in Table 4.1.
Values of Trigonometric Functions for Some Common Angles
Note that angles can be expressed in terms of degrees or radians. For example, a
circle has a total of 360 degrees, a straight line has 180 degrees, and a right angle
is 90 degrees. The same circle has 2p radians, a straight line has p radians, and a
right angle has ½ p radians. To convert an angle A expressed in degrees to radians,
multiply by the factor
p
180 .
To convert an angle in radians to degrees, multiply radians by the factor
180
p .
Values of the trigonometric functions for common angles are shown in Table 4.2.