Find sin θ

Question

if cot θ = - 4 and cos θ < 0

Answer 1

The value cot θ = - 4 and cos θ < 0.

Note that θ lies in Quadrant II because that is the only quadrant in which the cotangent and the cosine are negative.

Using the Pythagorean identity cosec² θ - cot² θ = 1, you obtain

cosec² θ - (- 4)² = 1

cosec² θ = 1 + 16 = 17.

Because cosecant is positive in Quadrant II, you can use the positive root to obtain

cosec θ = √(17).

Using the Reciprocal identity sin θ = 1/cosec θ = 1/√(17).

The trigonometric function value sin θ = 1/√(17).