# using the unit circle

• October 5th 2009, 09:34 AM
2clients
using the unit circle
Find all values of x on [0, 2pi] that satisfy the equation:

a) 2 cos(x)-1 b) 2sin^2(x) =1

I think I can somehow use the unit circle for this one, and the 2pi periods of the trig functions to find other possible answers that fit the domain, but I don't really know where to begin.

I would appreciate any tips,

Dave
• October 5th 2009, 10:29 AM
skeeter
Quote:

Originally Posted by 2clients
Find all values of x on [0, 2pi] that satisfy the equation:

a) 2 cos(x)-1 = ? b) 2sin^2(x) =1

(b) ...

$
2\sin^2{x} = 1
$

$
\sin^2{x} = \frac{1}{2}
$

$
\sin{x} = \pm \frac{1}{\sqrt{2}} = \pm \frac{\sqrt{2}}{2}
$

$
x = \frac{\pi}{4} \, , \, \frac{3\pi}{4} \, , \, \frac{5\pi}{4} \, , \, \frac{7\pi}{4}
$