Sections:

Trigonometric Identities and Equations, Page 7

Examples (continued)

Example 2:

If cos(theta) = 4/5, and θ is in quadrant I, what is the value of tan θ?

Procedure: 

  1. Choose an identity that involves the trigonometric functions given. For this problem, look for identities that involve cos and tan.
  2. Substitute the value of cos θ into the identities and solve for tan θ.


Solution: 

sec^2 (theta) = tan^2 (theta) + 1; 1/cos^2 (theta) = tan^2 (theta) + 1; 1/(4/5)^2 = tan^2 (theta) + 1; 1/(16/25) = tan^2 (theta) + 1; 25/16 - 1 = tan^2 (theta); 9/16 = tan^2 (theta); 3/4 = tan(theta)