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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.