Question

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

Answer 1

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

Answer 2

`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`