solve for x for angles between o and 360 degrees

Question

(i)cos2x+sinx=0

Answer 1

cos2x+sinx=0
(1 - 2sin^2 x) + sinx = 0
2sin^2 x - sinx - 1 = 0
(2sinx +1)(sinx - 1) = 0
sinx = -1/2 or sinx = 1

for sinx = -1/2, x is in quads III or IV
x = 210° or 330°
for sinx = 1
x = 90°

x = 90° , 210° or 330°