Question

Find sin x and cos x given that cot x=2 and cos x <0?

Answer 1

`sinx=-1/sqrt5, cosx=-2/sqrt5`.

Explanation:

Recall that, `csc^2x=1+cot^2x`.

`:. csc^2x=1+2^2=5`.

`:. cscx=+-sqrt5`.

But, `because cotx gt 0, and, cosx lt 0, sinx=1/cscx=-1/sqrt5`.

Finally, `cotx=cosx/sinx rArr cosx=sinx*cotx=-2/sqrt5`.