Let be an angle in quadrant III such that cos Find the exac

Let be an angle in quadrant III such that cos =- Find the exact values of csc and cot . cot =

Solution

cos theta=-2/5

theta is in third quadrant where tan and cot are positive

sin theta=sqrt(1-cos²theta) = -sqrt(1-4/25) = -sqrt(21)/5

csc theta=1/sin theta=-5/sqrt21

cot theta=cos theta/sin theta=2/sqrt21