Question

Given that cos θ ≈ −0.485, where 2 π < θ < π, find sin θ.

Answer 1

The answer to your question is: sin Ф = -0.8745

Explanation:

cos Ф = -0.485 π < Ф < 2π ; 180 < Ф < 360

Cosine is negative in the second and third quadrangle, but we need to find the quadrangle only in the third quadrangle.

cos Ф = adjacent side / hypotenuse

-0.485/ 1 = adjacent side / hypotenuse

adjacent side = -0.485

hypotenuse = 1

- Calculate the opposite side

c² = a² + b²

a² = c² - b²

a² = 1² - (-0.485)²

a² = 1 - 0.235

a² = 0.7648

Opposite side = a = - 0.8745, but is negative in the third quadrangle.

sin Ф = -0.8745 / 1

sin Ф = -0.8745