if cot x =-1/2 and sin x = 2√5/5, find cos x

Question

Use quotient and reciprocal identities to find the function value.

Answer 1

cot(x) = cos(x) /sin(x)

Therefore

cos(x) = cot(x) × sin(x) = (-1/2) × (2√5/5) = - √5/5

Note that the problem is over-specified.

The absolute value of cos(x) can be obtained from sin(x) alone

(using the identity six²(x) + cos²(x) = 1).

And the sign of cos(x) could be determined from only the sign of cot(x) without knowing its value.