find cot theta

Question

if cos theta = 2/3 and tan theta < 0

Answer 1

The angle is in the second quadrant, and the the cos is negative.

Sin²θ + cos²θ =1

Sin²θ = 1 - 4/9 = 5/9

sin θ =√(5/9)

sin θ = √5/3

Tan θ = sinθ/cosθ

Tan θ = - ((√5/3)/(2/3))

Tan θ = - (√5/2)

cot θ = 1/tanθ = - (2√5) / 5