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#