If cosθ = -5/13 and 0 <= θ <= 2π, what are possible values of θ?

[Ace.]

Homework Statement

If cosθ = -5/13 and 0 <= θ <= 2π, what are possible values of θ?

Homework Equations

The Attempt at a Solution

θ is in quadrant 2 or 3

in quadrant 2:
related acute = cos^{-1}(5/13)
= 1.18
θ = π - 1.18
= 1.96 radians

in quadrant 3:
related acute angle = 1.18
θ = π + 1.18
= 4.32 radians

Those are the two values I got for θ. But my book says the answer is 5.14. Can you tell me where I am going wrong?

 

[Mentallic]

Where didn't you go wrong?

Nah, I'm just kidding The book's answer is wrong, you're right. They accidentally included the angle in the 4th quadrant rather than the 3rd as you've correctly done.