Same angle trigonometry function example

Question:

The angle a lies in Quadrant2, and tan a = -3/4. Find the value of cos a.

Solution:

By the definition, tan a = sin a/cos a. Given tan a = -3/4. So, sin a/cos a = -3/4. Therefore, sin a = - (3/4) cos a. Using the formula, sin²a + cos²a = 1. So, (-3 cos a/4)² + cos²a = 1. We get cos²a = 16/25. Since the angle a lies in Quadrant2, so the value of cos a is negative, so cos a = -4/5. For a detailed solution, please watch the video.