Defining Other Trigonometric Functions

These functions are defined everywhere except where there is a division by zero. They are periodic with period 2π. Their graphs are shown in Figure 7.1.10.

Figure 7.1.10

When θ is strictly between 0 and π/2, trigonometric functions can be described as the ratio of two sides of a right triangle with an angle θ. Let a be the side opposite θ, b the side adjacent to 9, c the hypotenuse as in Figure 7.1.11.

Figure 7.1.11

Comparing this triangle with a similar triangle whose hypotenuse is a radius of the unit circle, we see that