Question

If cos ⁡θ=−8/17, and 180°θ<270°, what is sin θ?

Answer 1

-15/17

Explanation:

One method is to use Pythagorean identity.

sin² θ + cos² θ = 1

sin² θ + (-8/17)² = 1

sin² θ + 64/289 = 1

sin² θ = 225/289

sin θ = ±15/17

Since θ is in the third quadrant, sin θ < 0. So sin θ= -15/17.

Another method is to draw a triangle in the third quadrant, with angle θ, adjacent side -8, and hypotenuse 17. Use Pythagorean theorem to find the opposite side:

c² = a² + b²

17² = (-8)² + b²

b = -15

Therefore, sin θ = -15/17