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30 Part I: Technical Mathematics
Table 4.2 Values of trigonometric functions for common angles.
Part I.D
Angle in Angle in
degrees radians Sine Cosine Tangent Cotangent Secant Cosecant
0 0 0 1.000 0 Undefined 1.000 Undefined
30 1/6 p 0.5000 0.8660 0.5774 1.7321 1.1547 2.000
45 1/4 p 0.7071 0.7071 1.000 1.000 1.4142 1.4142
60 1/3 p 0.8660 0.5000 1.7321 0.5774 2.000 1.1547
90 1/2 p 1.000 0 Undefined 0 Undefined 1.000
Trigonometric Identities
Some useful trigonometric identities include the following:
sin
( A)+ cos ( A)=
1
2 2
2 2
1 + tan ( A)= sec ( A)
2
1 cot A csc 2 A
+ ( )= ( )
To find the cosine of an angle A when the sine of the angle is known, we can use
the first identity as follows:
2 2
sin ( A)+ cos ( A)=
1
2 2
cos ( A)= 1 sin ( A)
2
2
cos ( A) = 1 sin ( A)
cos
2
( A)= 1 sin ( A)
For example, for the angle A = 30 degrees with sine (30) known to be 0.5:
sin
( A)+ cos ( A)=
1
cos ( A)= 1
0.
5
2 2
2 2
( ) = 5
2
cos A 1 0.
cos ( A)=
0.
866
SOLVING FOR UNKNOWN SIDES AND ANGLES
OF A RIGHT TRIANGLE
Using the six basic trigonometric functions and the Pythagorean theorem, we
can find the length of the unknown sides of a triangle, given the values of one
2