Question

Question #eb243

Answer 1

`sin x = +- sqrt5/5`

Explanation:

Use trig identity:
`sin^2 x = 1/(1 + cot^2 x)`
In this case:
Call x the arctan (1/2)
`tan x = 1/2` --> `cot x = 1/(tan) = 2`
`sin^2 x = 1/(1 + 4) = 1/5`
`sin x = +- 1/(sqrt5) = +- sqrt5/5`
Because `tan x = 1/2`, x could be either in Quadrant 1 or in Quadrant 3.
There fore, sin x could be either positive or negative.