sin tan finding tan precalculus

Question

If sin theta = -(5/13) for 90 degrees < theta!< 270 Degrees , then what does tan theta equal?

Answer 1

If sinθ = -(5/13) for 90° < θ < 270° , then what does tanθ equal?

 

tanθ  = sinθ /cosθ

 

So we need to find cosθ.

 

sin²θ + cos²θ = 1

 

cos²θ = 1 - sin²θ

 

cos²θ = 1 - (-5/13)²

 

cos²θ = (169/169) - (25/169) = 144/169

 

cosθ = ±12/13

 

In the interval 90° < θ < 270°, the cosine is negative, so cosθ = -12/13

 

tanθ = sinθ/cosθ = ?