If costheta squareroot 54 and is in the fourth quadrant fin

If cos(theta) = squareroot 5/4, and is in the fourth quadrant, find the exact values for sin(theta) and tan(theta), (Partial credit for decimal approximations.)

Solution

cos theta= -sqrt5 / 4

adjacent=sqrt5    and hypotenuse=4

therefore opposite= sqrt(4^2 - sqrt5 ^2)= sqrt 11

In fourth quadrant ,sin theta is negative

sin theta=opposite/hypotenuse= -sqrt11/4

tan theta=opposite/adjacent=-sqrt11/sqrt5= -sqrt55/5