Question

Given that the sec A = 13/5 and A is in QIV, determine exact value for the sin A.

Answer 1

The exact value of sin A is opp/hyp = -12/13

Explanation:

If A is in Quadrant IV then the "opposite side" is negative and the "adjacent side" is positive. Since sec A = hyp / adj = 13 / 5 and since opp^2 + adj^2 must add up to hyp^2, Therefore y = √(hyp^2 - adj^2), or

y = -√(13^2 - 25) = -√144 = 12.

The exact value of sin A is opp/hyp = -12/13