Solve cos2 w 7 sinw for all solutions 0 lessthanorequalto w

Solve cos^2 (w) = -7 sin(w) for all solutions 0 lessthanorequalto w

Solution

given cos²(w)=-7sin(w)

1-sin²(w)=-7sin(w)

sin²(w)-7sin(w)-1=0

sin²(w)-7sin(w)=1

sin²(w)-7sin(w) +(7/2)²=1 +(7/2)²

(sin(w) -(7/2))²=1 +(49/4)

(sin(w) -(7/2))²=(53/4)

(sin(w) -(7/2))=-(53 /2),(sin(w) -(7/2))=(53 /2)

sin(w) =(7-53)/2,sin(w) =(7+53)/2

sin(w) =(7+53)/2 =>no solution

sin(w) =(7-53)/2

=>w=sin^-1((7-53)/2)

=>w =3.28 ,6.14