Odd Function Problem  TOPIC_SOLVED

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

Re: Odd Function Problem

Postby Martingale on Mon Aug 23, 2010 12:45 am

burnbird16 wrote:But that's what I had originally, and I can't solve for y. Please, explain.


you can't solve...

Martingale wrote:
we know

so replace with

and solve for


for

subtract the then take the square root of both sides.
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Re: Odd Function Problem

Postby burnbird16 on Mon Aug 23, 2010 12:46 am

Oh, wait, I think I get it! do , then solve that for y! Awesome. Now, I only have one more problem...but it's in six parts. Basically, they are using simple trigonometric identities to create new ones. But I don't know how to get there. For example, I am to produce using
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Re: Odd Function Problem

Postby Martingale on Mon Aug 23, 2010 12:55 am

burnbird16 wrote:Oh, wait, I think I get it! do , then solve that for y! Awesome. Now, I only have one more problem...but it's in six parts. Basically, they are using simple trigonometric identities to create new ones. But I don't know how to get there. For example, I am to produce using



let

and use the fact that

and
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Re: Odd Function Problem

Postby burnbird16 on Mon Aug 23, 2010 12:59 am

Ah, okay, makes sense. Well, I'm gonna get to work on this, and I'll be back shortly. Again, thank you for all of your help, I couldn't have done this without your and Stapel's guidance.
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Re: Odd Function Problem

Postby burnbird16 on Mon Aug 23, 2010 1:42 am

Ugh, yet more issues arise.

How do I produce using the same identity as before? Also, how would I produce ?
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Re: Odd Function Problem

Postby Martingale on Mon Aug 23, 2010 2:38 am

burnbird16 wrote:Ugh, yet more issues arise.

How do I produce using the same identity as before?


let

so you get ...



now add and subtract a into the right hand side of the equation




then group the terms the right way and use the Identity to get the identity you want
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Re: Odd Function Problem

Postby Martingale on Mon Aug 23, 2010 2:41 am

burnbird16 wrote:Ugh, yet more issues arise.

How do I produce using the same identity as before? Also, how would I produce ?


to get

take



let

then solve for the cosine that is on the right hand side.
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Re: Odd Function Problem

Postby burnbird16 on Mon Aug 23, 2010 2:46 am

Th-th-th-th-th-th-th-th-that's all, folks! :D Thanks for all of your help, again, that finishes out the packet!
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Re: Odd Function Problem

Postby burnbird16 on Mon Aug 23, 2010 2:58 am

One tiny question though. How does the absolute value come into play? I'm to that point, but I don't understand the purpose of the absolute value there, or how to get it there.
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Re: Odd Function Problem  TOPIC_SOLVED

Postby Martingale on Mon Aug 23, 2010 3:04 am

burnbird16 wrote:One tiny question though. How does the absolute value come into play? I'm to that point, but I don't understand the purpose of the absolute value there, or how to get it there.



for example .... suppose we have the function

taking the square root of both sides gives a new function...

then


look what happens when we put in a few values






let


so no matter what number I put in I get the positive version back...well...that is the absolute value function.

ie
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