Question

How do you find sin if tan is 4?

Answer 1

See below

Explanation:

We know that `sin^2x+cos^2x=1`

Dividing by `cos^2x` last identity we have

`tan^2x+1=sec^2x=1/cos^2x`

Then `16+1=1/cos^2x` then `cos^2x=1/17`

And applying first identity

`sin^2x+1/17=1`

`sin^2x=1-1/17=16/17`

`sinx=sqrt16/sqrt17=4/sqrt17`

Answer 2

`sin x = +- 4/sqrt17 = (4sqrt17)/17`

Explanation:

Use trig identity:
`sin^2 x = 1/(1 + cot^2 x)`
In this case tan x = 4 --> `cot x = 1/4`
`sin^2 x = 1/(1 + 1/16) = 16/17`
`sin x = +- 4/sqrt17`
tan x = 4 --> x could be in Quadrant 1 or Quadrant 3, therefor
sin x could be positive or negative.