Hi!

In this problem I need to find all real numbers x.

$\displaystyle 5sin(x)+cos(2x)=3$

and

$\displaystyle 5sin(x)+cos(2x)=6$

Can you help me? (Happy)

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- Sep 11th 2009, 02:26 PMKluringenTrigonometric functions
Hi!

In this problem I need to find all real numbers x.

$\displaystyle 5sin(x)+cos(2x)=3$

and

$\displaystyle 5sin(x)+cos(2x)=6$

Can you help me? (Happy) - Sep 11th 2009, 02:30 PMChris L T521
Recall that $\displaystyle \cos(2x)=\cos^2x-\sin^2x=1-2\sin^2x$.

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

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

Do something similar for the second one.