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

In summary, the person is asking for help with 15 identities problems from someone who is an expert summarizer of content. The person provides a summary of the content and ends the output with "In summary, these are the formulas to know: sin(2t), cos(2t), sin(3x), cos(3x), sin(2theta), cos(2theta), and cos(t)."
  • #1
spedman
3
0
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 [Broken]

http://img509.imageshack.us/img509/9642/math2fw6.jpg [Broken]

http://img70.imageshack.us/img70/7996/math3hn7.jpg [Broken]

http://img69.imageshack.us/img69/7543/dsc00180on3.jpg [Broken]


Thanks for any help on any of them you can give.
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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)
 
  • #6
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.
 
  • #7
http://img69.imageshack.us/img69/7543/dsc00180on3.jpg [Broken]

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 [Broken]

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
 
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  • #8
spedman said:
http://img69.imageshack.us/img69/7543/dsc00180on3.jpg [Broken]

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:

[tex]sinP + sinQ=2sin(\frac{P+Q}{2})cos(\frac{P-Q}{2})[/tex]

and

[tex]cosP + cosQ=2cos(\frac{P+Q}{2})cos(\frac{P-Q}{2})[/tex]
 
Last edited by a moderator:
  • #9
rock.freak667 said:
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:

[tex]sinP + sinQ=2sin(\frac{P+Q}{2})cos(\frac{P-Q}{2})[/tex]

and

[tex]cosP + cosQ=2cos(\frac{P+Q}{2})cos(\frac{P-Q}{2})[/tex]

actually it doesn't help in that question's case. finding sin3x is faster.
 
  • #10
[tex]\frac{sin3x+sinx}{cos3x+cosx}

=\frac{2sin2xcosx}{2cos2xcosx}=tan2x[/tex]
 
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  • #11
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.
 
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  • #12
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.
 

What are trigonometric identities?

Trigonometric identities are mathematical equations that involve the trigonometric functions (sine, cosine, tangent, etc.) and are true for all values of the variables involved.

Why are trigonometric identities important?

Trigonometric identities are important because they allow us to simplify and manipulate trigonometric expressions, making it easier to solve mathematical problems involving angles and triangles.

What is the most commonly used trigonometric identity?

The most commonly used trigonometric identity is the Pythagorean identity, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

How do you prove trigonometric identities?

Trigonometric identities can be proven using algebraic manipulations and properties of triangles. We can also use the double angle, half angle, and sum and difference identities to prove other identities.

What are some real-life applications of trigonometric identities?

Trigonometric identities are used in a variety of fields, including engineering, physics, and astronomy, to solve problems involving angles and waves. They are also used in navigation and GPS technology to calculate distances and angles between locations.

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