Question

If `tan theta=2/3` and `cos theta >`, how do you find `sin theta`?

Answer 1

`sin t = (2sqrt13)/13`

Explanation:

`tan t = 2/3` -->
`cot t = 1/(tan t) = 3/2`
`sin^2 t = 1/(1 + cot^2 t) = 1/(1 + 9/4) = 4/13`
`sin t = +- 2/sqrt13`
Because tan t > 0 and cos t > 0, therefor, t lies in Quadrant 1 -->
and sin t is positive
`sin t = (2sqrt13)/13`