Sections:

Trigonometric Identities and Equations, Page 4

Quotient Identities

The next set of identities is called quotient identities.

For all values of theta, (where defined), the following are true:

sine of theta over cosine of theta equals tangent of theta; cosine of theta over sine of theta equals cotangent of theta

Let’s take a closer look at tan(theta) = sin(theta)/cos(theta). Remember the triangle from the unit circle? 

5.3.4 graphic 1

You know that sin(theta) = y/1 and cos(theta) = x/1 You also know that tan(theta) = y/x.

sin(theta)/cos(theta) = (y/1)/(x/1) = y/1 * 1/x = y/x. Therefore: tan(theta) = sin(theta)/cos(theta).