Anaylytic Trig: Using dbl-angle formulas...

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frauleinedoctor

Junior Member
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Jan 9, 2009
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I have the first step I think, I've just run out of gas from there.

I am supposed to find the exact values of sin 2u, cos 2u, and tan 2u using the dbl angle formulas for this problem:

sin u = 3/5, when 0 < u < pi/2

What am I supposed to do? How do these formulas help me here?
 
frauleinedoctor said:
I have the first step I think …
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That's nice. Are you trying to keep it secret?

If not, then please share your thoughts. The more information that you provide in your posts here, the better that others can figure out where you're at and what you need.

-
… What am I supposed to do? How do [the double-angle] formulas help me here?
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(I'm wondering if you looked at the double-angle formulas.)

They've given you the exact value of sin(u).

They've given you enough information to find the exact value of cos(u).

Knowing both sin(u) and cos(u) is sufficient to find the exact value of tan(u).

All of the double-angle formulas require knowing nothing other than sin(u), cos(u), and tan(u).

You are supposed to substitute the exact values for sin(u), cos(u), and tan(u) into each double-angle formula as needed.

After that, it's just arithmetic.

Please show your work, if you need more help with this exercise. If you can't do the work for any particular step, then please post your reasoning, so that I have a clue as to why you're stuck.

 
Mm...but that would be for just cosu = 4/5.

cos *2* u....Welll, that would have to be different, right?
 


When I read some of your posts after my initial post, I wonder if you read what I typed.

If I write something that you do not understand, then you need to let me know.

Please stop making wild guesses.

I want you to look up the double-angle formulas, and post them here so that I know that you've at least looked at them.

I will not provide any more help to you on this exercise until after you post the double-angle formulas.

 
Ok.



sin 2u = 2 sin u cos u

cos 2u = cos^2 u - sin^2 u
or = 2 cos^2 u - 1
or = 1 - 2 sin^2 u

tan 2u = 2 tan u / 1 - tan^2 u
 
frauleinedoctor said:
Would this work:


sin(2u) = 2 (3/5) (4/5) ?
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Exactly.

Now, it's just a matter of doing the arithmetic.

You have a choice of formulas for calculating the value of cos(2u). Use whichever one you prefer. Or, use all three, and see if you get the same value from each. (You should.)

 
Nevermind that.




Ok, I don't understand how 4/5 , or cosu , fits into these formulas. Do I merely substitue it in for u? Thats the only thing I can think to do, but that doesn't seem to lead me toward where I want to go...In other words, I don't see how the problem would reduce like that.

i.e.


cos 2u = cos^2 (4/5) - sin^2(3/5)


Is that right?
 
frauleinedoctor said:
… cos(2u) = cos^2(4/5) - sin^2(3/5)

Is that right?
Click to expand...


Nope.

This is the same mistake that I explained to you yesterday.

You changed the angle from u to 4/5 on the cosine term.

You changed the angle from u to 3/5 on the sine term.

The angle u is neither 4/5 nor 3/5.

It is the cosine of angle u that is 4/5.

That's why you previously got cos(u) = 4/5.

It is the sine of angle u that is 3/5.

That's why they gave you sin(u) = 3/5.

Here's the correct substitutions for cos(u) and sin(u) in that particular formula for cos(2u):

cos(2u) = (4/5)^2 - (3/5)^2

 
Ohh, ok that makes sense, Its all one term/variable.


Ok, I see how this works out then.


Its works out to cos2sin = 7/25.
 
frauleinedoctor said:
… [It] works out to cos2sin = 7/25.
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Hooboy. :roll:

Well, you got the 7/25 part correct, anyway.

(Your mind might make a fascinating case study, Fräulein Doktor. By the way, the address "Fäulein" is quite outdated; unless you're trying to make some reference to the 1940 film.)

Dogs are pulling me by the left pantleg out the front door. Gotta go.



 
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