Pythagoream Identities

Question

Find cot x if cos x= 1/7 and sin x <0

Answer 1

sin²x = 1 - cos²x

Using sin x < 0, sin x = -√(1 - cos²x) = -√48 / 7 = -4√3/7

cotx = cos(x) / sin(x) = (1/7) / (-4√3/7) = -1/4√3 = -√3 /12

Answer 2

sin² + cos² = 1

Then select the negative value for sine.