how can I solve cos2x+sinx=0 ?

Question

how can I solve this problem:

cos2x + sinx = 0

thank you

Answer 1

cos(2x)+sin(x)=0,

1-2sin²(x)+sin(x)=0,

2sin²(x)-sin(x)-1=0,

(2sin(x)+1)(sin(x)-1)=0,

sin(x)=-½, x=-π/6 or -30º.

The more general answer is x=2πn-π/6, or 360n-30 degrees, where n is an integer. Also 7π/6+2πn (360n+210 degrees).

Also, sin(x)=1, so x=π/2 (90º) or, more generally, 2πn+π/2.