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:

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

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! :)

Thanks in advance!

Rhys.

Re: help with this trig identity problem

$\displaystyle \sin^2 x = 1 - \cos^2 x$

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

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

Can you go from there?

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$\displaystyle -2cos^2x$ or ignore it and use the sum to product formula on the whole thing? I am not sure. :(

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$\displaystyle -2cos^2x$ 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 $\displaystyle \cos^2 x$ to $\displaystyle \frac{1 + \cos 2x}{2}$ 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?

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?

Re: help with this trig identity problem

or should i factor?

Also: I cant find the trig identity that you used anywhere, the$\displaystyle sin^2 x= 1-cos^2 x$ 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

Re: help with this trig identity problem

Ah, so is it the $\displaystyle sinx = sqrt*(1-cos^2 x)$ 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 :)

Re: help with this trig identity problem

Quote:

Originally Posted by

**Rhys101** Ah, so is it the $\displaystyle sinx = sqrt*(1-cos^2 x)$ 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, $\displaystyle \sin x$ might not equal $\displaystyle \sqrt{1 - \cos^2 x}$. It could equal $\displaystyle -\sqrt{1 - \cos^2 x}$. Better to leave it as $\displaystyle sin^2 x$.

Great job with the correct answer.