Question

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

Answer 1

Answer:

$cos\theta =-\frac{12}{13}$

Step-by-step explanation:

$tan\theta =\frac{sin \theta}{cos \theta}$

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

We have sin²θ + cos²θ = 1

That is

           $\left ( \frac{-5}{13} \right )^2+cos^2\theta =1\\\\cos^2\theta =1-\frac{25}{169}=\frac{144}{169}\\\\cos\theta =-\frac{12}{13}$

Answer 2

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)