Trigonometry Question

Question

If sin θ = 12/13, and cos θ > 0, find tan θ

a. 12/5

b. -12/5

c. 5/12

d. -5/12

I got answer A.

Answer 1

sin(theta) = 12/13

cos(theta) = 5/13 since 13 squared - 12 squared = 25 = 5 squared. -5 squared also = 25, but since cosine is positive, that eliminates -5.

tan(theta) = sin(theta)/cos(theta) = (12/13)/(5/13) = 12/5

Answer 2

This is a 5-12-13 triangle (one of the Pythagorean triples). opp = 12, adj = 5, hyp = 13. Tan = opp/adj, so 12/5. Now we get to deal with quadrants. Sin is positive in quadrants I and II, and it indicates that cos is positive, and cos is positive in Quadrants I and IV. The only overlap is in Quadrant I, which is where tan is also positive. Your answer is correct.