# help with this trig identity problem

• Nov 9th 2012, 02:54 PM
Rhys101
help with this trig identity problem
Hi all again!

Hoping you can help me with this one as I dont really have a clue how to go about it properly:

$2sin^2 x + 3cos x-3=0$

Ive used all kinds of identities and get really long and nonsensical answers, if someone could take me through step by step that would be ideal;
I have the answer, I just need to know how to arrive at it! :)

Rhys.
• Nov 9th 2012, 02:57 PM
richard1234
Re: help with this trig identity problem
$\sin^2 x = 1 - \cos^2 x$

$2(1 - \cos^2 x) + 3 \cos x - 3 = 0$

$-2 \cos^2 x + 3 \cos x - 1 = 0$

Can you go from there?
• Nov 9th 2012, 03:05 PM
Rhys101
Re: help with this trig identity problem
Wow, that was fast!
Thanks, umm no not really, should I use the power reducing formula for the $-2cos^2x$ or ignore it and use the sum to product formula on the whole thing? I am not sure. :(
• Nov 9th 2012, 04:32 PM
richard1234
Re: help with this trig identity problem
Quote:

Originally Posted by Rhys101
Wow, that was fast!
Thanks, umm no not really, should I use the power reducing formula for the $-2cos^2x$ or ignore it and use the sum to product formula on the whole thing? I am not sure. :(

You don't need any more trig identities from here. In fact, reducing $\cos^2 x$ to $\frac{1 + \cos 2x}{2}$ makes it even worse because you have a cos 2x and cos x in the same equation. Basically, the question can now be solved using just algebra. Do you see how?
• Nov 9th 2012, 08:09 PM
Rhys101
Re: help with this trig identity problem
Of course! I am so dense! It's a quadratic, so I just use the quadratic formula to find cos x, yes? Will other other questions be similar to this? With the use of only one trig identity and doing the rest via algebra? Is it likely that with most equations I first have to make all the trig values the same so I can use them as a variable?
• Nov 9th 2012, 08:32 PM
Rhys101
Re: help with this trig identity problem
or should i factor?
Also: I cant find the trig identity that you used anywhere, the $sin^2 x= 1-cos^2 x$ would you be able to find me a link where this one is stashed? :) There might be others there I am missing and don't know about.

Thanks again
• Nov 9th 2012, 08:51 PM
Rhys101
Re: help with this trig identity problem
Ah, so is it the $sinx = sqrt*(1-cos^2 x)$ but because of the power of 2 on the sin it cancels the square root? Also I factored and came up with the right answer :)
• Nov 10th 2012, 05:24 AM
richard1234
Re: help with this trig identity problem
Quote:

Originally Posted by Rhys101
Ah, so is it the $sinx = sqrt*(1-cos^2 x)$ but because of the power of 2 on the sin it cancels the square root? Also I factored and came up with the right answer :)

Careful, $\sin x$ might not equal $\sqrt{1 - \cos^2 x}$. It could equal $-\sqrt{1 - \cos^2 x}$. Better to leave it as $sin^2 x$.

Great job with the correct answer.