# Math Help - Trig problem...

1. ## Trig problem...

I'm stuck on this problem...

Find all solutions in the interval [0,2π]: 1 - sinx = 2 cos^2x

any help would be appreciated.

I'm stuck on this problem...

Find all solutions in the interval [0,2π]: 1 - sinx = 2 cos^2x

any help would be appreciated.
$2\cos^2{x} = 2(1 - \sin^2{x})$

sub that into the original equation for $2\cos^2{x}$ and solve the resulting quadratic in $\sin{x}$

3. ## Trig equation

I'm stuck on this problem...

Find all solutions in the interval [0,2π]: 1 - sinx = 2 cos^2x

any help would be appreciated.
Use the identity $\cos^2x = 1-\sin^2x$ and then re-arrange as a quadratic in $\sin x$:

$1 - \sin x = 2(1-\sin^2x)$

$\Rightarrow 2\sin^2 x -\sin x -1 = 0$

$\Rightarrow (\sin x - 1)(2\sin x +1) = 0$

$\Rightarrow \sin x = 1$ or $\sin x = -\tfrac{1}{2}$

I'll leave these to you.