Precalculus question

Question

If tanθ= - 12/5 and θ lies in quadrant 2, then what is the value of cos 2θ? 

Answer 1

If tanθ= - 12/5, x= -5 and y = 12.

To find r, use the Pythagorean Theorem:

r² = x² + y²

r² = (-5)² + 12²

r² = (-5)² + 12²

r² = 25 + 144

r² = 169

r = 13

Therefore sin θ = 12/13.

To evaluate cos 2θ, we can use the Double Angle Identity:

cos 2θ = 1 - 2•sin²θ

Substitute the value of sin θ:

cos 2θ = 1 - 2•(12/13)²

cos 2θ = 1 - 2•(144/169)

cos 2θ = 1 - 288/169 =169/169 - 288/169

cos 2θ = -119/169