Solve 8 cos2w 2sinw 7 0 for all solutions 0 lessthanorequ

Solve 8 cos^2(w) - 2sin(w) - 7 = 0 for all solutions 0 lessthanorequalto w lessthanorequalto 2 pi w = Give your answers accurate to 2 decimal places, as a list separated by commas

Solution

8cos^2 w -2sin w-7=0

8-8sin^2 w -2sin w-7=0

8sin^2 w +2sin w-1=0

8sin^2w +4sinw-2sinw-1=0

4sinw(2sinw+1)-1(2sinw+1)=0

(4sinw+1)(2sin w+1)=0

Sin w=1/4, sin w=-1/2

w=.25,2.89,7pi/6,11pi/6