If tanθ = 5/12 and π < θ < 2π, what is cosθ?

Correct answer: c −12/13

tan is positive and θ is in the 3rd quadrant; x = −12, r = 13; cosθ = −12/13.

Why the other options are wrong

• a 12/13: 12/13 is positive; tanθ positive with π < θ < 2π puts θ in the 3rd quadrant, where cos is negative.
• b 5/13: 5/13 is |sinθ|; it is a different quantity from the one asked for.
• d −5/12: −5/12 mixes x and y; cosθ = x/r = −12/13.