Question

Find cos θ if sin θ = -(5/13) and tan θ > 0

Answer 1

Remember:

sin²x + cos²x = 1

(-5/13)² + cos²θ = 1

(25/169) + cos²θ = 1

cos²θ = 1 - (25/169)

cos²θ = (144/169)

tan θ > 0 ⇒ cosθ = negative

cosθ = -√(144/169)

cosθ = -(12/13)

Answer 2

`cos\theta =-(12)/(13)`

Explanation:

`tan\theta =(sin \theta)/(cos \theta)`

If tan θ > 0 and sin θ < 0 then cos θ <0

We have sin²θ + cos²θ = 1

That is

`\left ( (-5)/(13) \right )^2+cos^2\theta =1\\\\cos^2\theta =1-(25)/(169)=(144)/(169)\\\\cos\theta =-(12)/(13)`