Can you help me with these tricky trigonometric identities for my math final?

[spedman]

I need some help on 15 identities problems to help me study for my math final.

They are blurry and somewhat hard to read, but if anyone wants to take a crack at some of them they are here:

http://img407.imageshack.us/img407/5696/math1lh2.jpg

http://img509.imageshack.us/img509/9642/math2fw6.jpg

http://img70.imageshack.us/img70/7996/math3hn7.jpg

http://img69.imageshack.us/img69/7543/dsc00180on3.jpg


Thanks for any help on any of them you can give.

 

[rocomath]

https://www.physicsforums.com/showthread.php?t=94384

You must show effort in order to receive help, we're not here to do your hw.

 

[spedman]

I know that, and I wanted to say it there, but I wasn't sure if anyone would believe me, but this isn't homework, merely just something to help me study for my final on Thursday.

 

[Avodyne]

We *still* want to see some attempts on your part to work them out.

And, we don't want to read blurry gray-on-gray pages. Take the trouble to type them in, if you want us to type something in response.

 

[spedman]

Ok, I'll ask more help oriented questions.

The problem is:

sin2t-cott = -cott cos2t

if solving from the left side, does

sin2t-cott = 2sintcost- (cost/sin)

 

[Avodyne]

Yes. Now let's work on the right side. We have
cos(2t)=cos^2(t)-sin^2(t)=2cos^2(t)-1=1-2sin^2(t)
Which of these is likely to be the most useful? If you don't know, try all three; multiply each by -cot(t) = -cos(t)/sin(t) and see what you get.

 

[shawshank]

http://img69.imageshack.us/img69/7543/dsc00180on3.jpg

For this one, you need to first figure out the sin 3x in terms of sin x (and cos3x in terms of cos x). Once you have done that, substitute them in and it will be rather easy.

http://img407.imageshack.us/img407/5696/math1lh2.jpg

Second one from the top, let 2theta = x and solve for x. very simple.

On this one, third from the top. Remember what wonders you can do with cos^2 x and sin^2 x, especially on the left side. What two things multiply to give you cos^4 x?

I think the rest are easy, just mention any other ones you are having difficulties with I don't want to go through all, it's late :D

 

[rock.freak667]

http://img69.imageshack.us/img69/7543/dsc00180on3.jpg

For this one I suggest you use the factor formulas as these are most helpful when given problems like this.

these are the formulas to know:

$$sinP + sinQ=2sin(\frac{P+Q}{2})cos(\frac{P-Q}{2})$$

and

$$cosP + cosQ=2cos(\frac{P+Q}{2})cos(\frac{P-Q}{2})$$

 

[shawshank]

For this one I suggest you use the factor formulas as these are most helpful when given problems like this.

these are the formulas to know:

$$sinP + sinQ=2sin(\frac{P+Q}{2})cos(\frac{P-Q}{2})$$

and

$$cosP + cosQ=2cos(\frac{P+Q}{2})cos(\frac{P-Q}{2})$$

actually it doesn't help in that question's case. finding sin3x is faster.

 

[rock.freak667]

$$\frac{sin3x+sinx}{cos3x+cosx} =\frac{2sin2xcosx}{2cos2xcosx}=tan2x$$

 

[unplebeian]

I highly doubt if you are 'preparing' for your exam'. Sorry for the bluntness, but most of these are just 2 to 3 step solutions.

I think you need to know some of the identities. Some are mentioned above, here are a few more

sin (2t)= 2sin(t) cos (t)
1-cos(t)= 2 sin^2(t/2)

You just need to be familiar with the identities and then when you see it later on in life, you'll automatically know what to do.

 

[Dr Transport]

The easiest way to attack these problems is to convert ALL the quantities into sines and cosines before doing anything, simplify them from there and rearrange. Many of these will be solved in less than 10 lines.