Question

How do you find y if the point (5,y) is on the terminal side of theta and `costheta=5/13`?

Answer 1

`y = +- 12`

Explanation:

`cos t = 5/13`
`sin t = y/13`
Use trig identity:
`sin^2 t + cos^2 t = 1`
`y^2/169 + 25/169 = 1`
`y^2 + 25 = 169`
`y^2 = 169 - 25 = 144`
`y = +- 12`
There are 2 arcs (or angles) t that have the same cos value (5/13).