Trig identities and equations

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Jellicorse
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Joined: Thu Jul 18, 2013 10:48 am
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Trig identities and equations

Postby Jellicorse » Thu Jul 18, 2013 11:02 am

I have been having a lot of problems with trig identities and their use in solving formulae, and wondered if anyone could help me out with this.

The following is an equation which I thought I had solved but my answer is different from that provided by my book, so I must have made a mistake. The problem is, I can't see where.

Solve the equation

One of my big difficulties with this kind of question is knowing which identity to use.

For example, in this question, saying means there are three possible starting points:



or



or

[


After looking at these three possibilities, I decided the second may be the best as everything is in terms of cos theta and it's quadratic...

=

And factorizing this:



So or [. The latter is outside the domain, so can be discounted.







But this is not what the books says the answer should be ()

I would really appreciate it if anyone could tell me what's going wrong here because these trig identities are really giving me a hard time..!

FWT
Posts: 121
Joined: Sat Feb 28, 2009 8:53 pm

Re: Trig identities and equations

Postby FWT » Thu Jul 18, 2013 5:41 pm

Jellicorse wrote:One of my big difficulties with this kind of question is knowing which identity to use.

If there's a shortcut or formula for knowing which ident to use, I've never heard of it. You got to try different ones until you find one that works. Sometimes you and a friend will use different ones but still come out to the same answer.

Jellicorse wrote:The following is an equation which I thought I had solved but my answer is different from that provided by my book, so I must have made a mistake. The problem is, I can't see where.

Solve the equation

For example, in this question, saying means there are three possible starting points:



or



or

[

After looking at these three possibilities, I decided the second may be the best as everything is in terms of cos theta and it's quadratic...

Yeh, that's what I'd do, too.

Jellicorse wrote: =

And factorizing this:


Nah: it's 5 not 7 so you need (2cos(@) + 1)(cos(@) - 3) = 0. Do the sign change & maybe it comes out right.

Jellicorse
Posts: 2
Joined: Thu Jul 18, 2013 10:48 am
Contact:

Re: Trig identities and equations

Postby Jellicorse » Fri Jul 19, 2013 12:46 pm

Thanks a lot FWT, that did lead to the correct solution...


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