Question

Given: Angle 0 is in quadrant III and sin0 = -sqrt(6)/4

Prove: cos0 = -sqrt(10)/4

Answer 1

Below.

Explanation:

The cosine is also negative in Quadrant III.

sin^2 O + cos^2 O = 1

cos^2 O = 1 - sin^2 O

= 1 - (-sqrt(6)/4)^2

= 1 - (6/16)

= 16/16 - 6 /16

= 10/16

So cos O = -sqrt(10/16)

= -sqrt(10)/4.