Question

How do you find sin if tan=2?

Answer 1

Find sin x knowing tan x = 2

Ans: `+- (2sqrt5)/5`

Explanation:

Use the trig identity: `sin^2 x = 1/(1 + cot^2 x)`
`tan x = 2` --> `cot x = 1/2` --> `cot^2 x = 1/4`
`sin^2 x = 1/(1 + 1/4) = 1/(5/4) = 4/5`
`sin x = +- 2/sqrt5 = +- (2sqrt5)/5`