Question

The angle θ lies in Quadrant IV . sinθ=−2/3 What is cosθ?

Answer 1

Consider this option:
1) if the angle belongs to IV quadrant, it means cos is in [0;1];
2)
`cos \alpha= √(1-sin^2 \alpha)`
using this formula cosθ=√(5/9) ⇒ cosθ=√5/3


`Answer: ( √(5))/(3)`

Answer 2

`cos(\theta) = (√(5))/(3)`

Explanation:

In the fourth quadrant, the sine is negative and the cosine is positive.

We also have that, for each angle
`\theta`,

`\sqrt{\sin^(2){\theta} + \cos^(2){\theta}} = 1`

So

`\sqrt{-((2)/(3))^(2) + \cos^(2){\theta}}^(2) = 1^(2)`

`\frac{4/9} + \cos^(2){\theta} = 1`

`\cos^(2){\theta} = (5)/(9)`

`cos(\theta) = (√(5))/(3)`