2sin^2(0)=sin(0)+1

Question

solve the equation for 0<0<360

Answer 1

let x=θ

2sin^2x=sinx+1

2sin^2x-sinx-1=0

factor

(2sinx+1)(sinx-1)=0

2sinx+1=0

2sinx=-1

sinx=-1/2

look on the unit circle

sin is -1/2 when x=7∏/6 or 210º (+∏k where k=0,±1,±2,...)

sinx-1=0

sinx=1

sin is 1 when x=∏/2 or 90º (+∏k where k=0,±1,±2,...)