# How do I solve this trig equation??

• Nov 16th 2009, 03:13 PM
dcowboys107
How do I solve this trig equation??
Find the EXACT solutions of the given equation in the interval [0,2π). If there is more than one answer, enter them in a list separated by commas. Decimal approximations and symbolic trigonometric expressions such as arctan(5) will be marked incorrect.

2sin^2(x)-5sin(x)+2=0

Where do I even begin on this? I'm lost and my professor has stopped coming because of an injury and I have a test Wendesday. I'd appreciate all the help I can get! Thanks so much in advance.
• Nov 16th 2009, 07:16 PM
Amer
Quote:

Originally Posted by dcowboys107
Find the EXACT solutions of the given equation in the interval [0,2π). If there is more than one answer, enter them in a list separated by commas. Decimal approximations and symbolic trigonometric expressions such as arctan(5) will be marked incorrect.

2sin^2(x)-5sin(x)+2=0

Where do I even begin on this? I'm lost and my professor has stopped coming because of an injury and I have a test Wendesday. I'd appreciate all the help I can get! Thanks so much in advance.

ok let u= sin x

$\displaystyle 2u^2 - 5 u +2 = 0$

$\displaystyle (2u-1)(u-2)$

$\displaystyle u= \frac{1}{2} \Rightarrow \sin x =\frac{1}{2} \Rightarrow x=\frac{\pi}{6} , x=\frac{5\pi}{6}$

$\displaystyle u-2 = 0 \Rightarrow \sin x = 2$ and this can't be true since sin x is bounded by -1 and 1