Suppose that Θ is in the fourth quadrant

Question

that cosΘ=1/3. what is the value of sinΘ?

Answer 1

The angle θ is in fourth quadrant.

Because cos θ > 0 in Quadrant IV, you can use the positive root to obtain cos θ = 1/3.

Using the Pythagorean identity sin² θ + cos² θ = 1, obtain

sin² θ + (1/3)² = 1

sin² θ + 1/9 = 1

sin² θ = 1 - 1/9 = (9 - 1)/9 = 8/9

Because sin θ < 0 in Quadrant IV, you can use the negative root to obtain sin θ = -√(8/9) =  -2√2/3.

Therefore,the value of sin θ =  -2√2/3.