To write sin x in terms of cos x use the relation `sin^2x + cos^2x=1`
=> `sin^2x = 1 - cos^2x`
Taking the square root of both the sides gives two values of sin x
`sin x = sqrt(1 - cos^2x)` and `sin x = -sqrt(1 - cos^2x)` . This makes it essential to know in which quadrant the angle x lies so that it can be determined if the value of sin x is positive or negative.
`sin x = sqrt(1 - cos^2x)` or `sin x = -sqrt(1 - cos^2x)` depending on which quadrant x lies in.