The cosine of the angle θ is -√7/3 if sinθ = √2/3
How to evaluate the cosine of the angle
From the question, we have the following parameters that can be used in our computation:
sinθ = √2/3
Using the following identity
sin²θ + cos²θ = 1
We have
(√2/3)² + cos²θ = 1
(2/9) + cos²θ = 1
This gives
cos²θ = 1 - (2/9)
cos²θ = (7/9)
The angle θ is in the second quadrant
So, we have
cosθ = -√7/3
Hence, the cosine of the angle is -√7/3