The Handy Math Answer Book

What are the same functions using a circle?

The following shows the same way of looking at the above triangle using a circle (also

see illustration):

• cos
  x/r


• sin
  y/r


• tan
  y/x


• sec
  r/x


• csc
  r/y


• cot
  x/y

What is an exampleof finding a trig function?

One example of finding a trig function—including an illustration—follows: Find the

trig functions of the angle 

60°. In this case, make a circle with a string extending

two units; then measure 60° from the vertex (O). Drop a line perpendicular from the

point on the circle to the initial line, creating a 90° angle; that makes the last angle

30°. Because the result is a right triangle, with the values of the hypotenuse (2) and

the adjacent leg (1), the Pythagorean Theorem (see elsewhere in this chapter) is used

to determine the length of the other leg, or a^2 b^2 c^2 :

12 b^2  22

1 b^2  4

b^2  3

202 b  3

Trigonometric functions can be used to describe a

right triangle.

Trigonometric functions of a circle.