Math Help - Trigonometric functions

1. Trigonometric functions

Hi!
In this problem I need to find all real numbers x.
$5sin(x)+cos(2x)=3$
and
$5sin(x)+cos(2x)=6$

Can you help me?

2. Originally Posted by Kluringen
Hi!
In this problem I need to find all real numbers x.
$5sin(x)+cos(2x)=3$
and
$5sin(x)+cos(2x)=6$

Can you help me?
Recall that $\cos(2x)=\cos^2x-\sin^2x=1-2\sin^2x$.

Thus, $5\sin x+\cos(2x)=3\implies 5\sin x+1-2\sin^2 x=3\implies2\sin^2 x-5\sin x+2=0$

Let $u=\sin x$. Then solve $2u^2-5u+2=0$, and then find $x$.

Do something similar for the second one.