Question

Find an expression for sin θ ?

Find an expression for sin θ in terms of x if cos θ =(x)/(x+1) .

Answer 1

`sin theta = +-sqrt(x^2+x+1)/(x+1)`

Explanation:

Pythagoras tells us:

`cos^2 theta + sin^2 theta = 1`

So:

`sin theta = +-sqrt(1-cos^2 theta)`

`color(white)(sin theta) = +-sqrt(1-(x/(x+1))^2)`

`color(white)(sin theta) = +-sqrt(((x+1)^2-x)/(x+1)^2)`

`color(white)(sin theta) = +-sqrt(x^2+x+1)/(x+1)`

Note that knowing the value of `cos theta` is not sufficient to determine the sign of `sin theta`.