What is the value of sin theta given that (5, 12) is a point on the terminal side of theta?

2 Answers
Jun 16, 2018

Hypotenuse of sqrt{5^2+12^2}=13 so sin theta = text{opp}/text{hyp} = 12/13

Jun 16, 2018

sin t = 12/13

Explanation:

Point (x = 5, y = 12) lies in Quadrant 1.
Call t the angle (or arc).
tan t = y/x = 12/5 --> cot t = 5/12
sin^2 t = 1/(1 + cot^2 t) = 1/(1 + 25/144) = 144/169
sin t = +- 12/13
Since t is in Quadrant 1, sin t is positive
sin t = 12/13