Find all real numbers θ in [0, 2π] such that sec θ = −2.

Question

I am not sure how to solve this problem even when looking at it's graph.

Answer 1

sec θ = -2

cos θ = -1/2, reference angle π/6.

 

What angle in QII and QIII have a reference angle of π/6?

Answer 2

If secant is -2, then cosine is -½ and you ought to be able to do that!.

 

On a graphing calculator, you could graph the cosine function and a second function y=-2 and find where they intersected.

 

There would be two values, one in Quadrant II, other in III. Knowledge of 30-60-90 reference triangles will help you to get exact answers, which is all you have to do because of the domain restriction stated in this problem.