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October 30, 2025, 06:06:25 pm
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Author Topic: Compound and Double angle help  (Read 2533 times)  Share 

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darkphoenix

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Compound and Double angle help
« on: April 02, 2010, 11:47:15 pm »
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Simplify each of the following expressions:

1a)

b)


Use double-angle formulas to find the exact value of:

a) sin
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kyzoo

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Re: Compound and Double angle help
« Reply #1 on: April 02, 2010, 11:55:22 pm »
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1.a)

cos(3x)cos(x) + sin(3x)sin(x)
= cos (3x - x) = cos 2x

b.)

sin(A+B)cos(A-B) - cos(A+B)sin(A-B)
= sin ((A+B) - (A-B))
= sin (A + B  - A + B)
= sin (2B)

And argh I need latex to do the last one =/
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darkphoenix

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Re: Compound and Double angle help
« Reply #2 on: April 03, 2010, 12:12:44 am »
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Wait is that your final answer? If so can you show the rest of your working please?
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mandy

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Re: Compound and Double angle help
« Reply #3 on: April 03, 2010, 12:30:39 am »
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Quote from: darkphoenix on April 02, 2010, 11:47:15 pm
Use double-angle formulas to find the exact value of:

a) sin

I'm not sure if this is what you're looking for, but:
Use


















Is that right?
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kyzoo

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Re: Compound and Double angle help
« Reply #4 on: April 03, 2010, 12:43:58 am »
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Quote from: darkphoenix on April 03, 2010, 12:12:44 am
Wait is that your final answer? If so can you show the rest of your working please?

...that is all my working 0.o

You just use the formulas
cos (A - B) = cos A cos B + sin A sin B
sin (A - B) = sin A cos B - sin B cos A
« Last Edit: April 03, 2010, 12:46:35 am by kyzoo »
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darkphoenix

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Re: Compound and Double angle help
« Reply #5 on: April 03, 2010, 12:49:06 am »
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Hm how did you get rid of the sin in the first one?

And cos in the second?
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kyzoo

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Re: Compound and Double angle help
« Reply #6 on: April 03, 2010, 12:52:37 am »
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Quote from: darkphoenix on April 03, 2010, 12:49:06 am
Hm how did you get rid of the sin in the first one?

And cos in the second?

cos (u - v) = cos u cos v + sin u sin v

Substitute u for 3x, and v for x

Hence you get cos (u - v) = cos (3x - x) = cos 2x

...

sin (u - v) = sin u cos v - sin u cos v

Substitute A + B for for u, and A - B for v

sin (u - v) = sin (A + B - (A - B)) = sin 2B

...

It's just a matter of learning the compound angle formulas. Once you've done that, they become 5 second questions.

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darkphoenix

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Re: Compound and Double angle help
« Reply #7 on: April 03, 2010, 03:32:56 pm »
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Ohh thanks alot man, wasnt thinking properly. Got it now.
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coletrain

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Re: Compound and Double angle help
« Reply #8 on: April 03, 2010, 06:12:05 pm »
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does compound angle and double angle formula come up in methods or just spesh?
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qshyrn

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Re: Compound and Double angle help
« Reply #9 on: April 03, 2010, 06:14:24 pm »
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Quote from: coletrain on April 03, 2010, 06:12:05 pm
does compound angle and double angle formula come up in methods or just spesh?
both.  but more in spesh
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AzureBlue

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Re: Compound and Double angle help
« Reply #10 on: April 03, 2010, 06:54:51 pm »
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Quote from: coletrain on April 03, 2010, 06:12:05 pm
does compound angle and double angle formula come up in methods or just spesh?
Comes in General Maths (S) and probably MM 3/4. These formulae are awesome :)
« Last Edit: April 03, 2010, 06:57:30 pm by AzureBlue »
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the.watchman

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Re: Compound and Double angle help
« Reply #11 on: April 03, 2010, 08:52:56 pm »
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Yeah, these formulas have slipped into the MM study design :)
I agree, they are awesome!
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stonecold

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Re: Compound and Double angle help
« Reply #12 on: April 03, 2010, 08:53:55 pm »
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^they are rather awesome.

i just need to learn the tan ones now :)
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AzureBlue

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Re: Compound and Double angle help
« Reply #13 on: April 03, 2010, 09:38:58 pm »
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Quote from: the.watchman on April 03, 2010, 08:52:56 pm
Yeah, these formulas have slipped into the MM study design :)
I agree, they are awesome!
I don't think they're in 1/2... 1/2 sucks. Just sin, cos, tan graphs I think and the circle.
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the.watchman

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Re: Compound and Double angle help
« Reply #14 on: April 03, 2010, 09:49:28 pm »
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Quote from: AzureBlue on April 03, 2010, 09:38:58 pm
Quote from: the.watchman on April 03, 2010, 08:52:56 pm
Yeah, these formulas have slipped into the MM study design :)
I agree, they are awesome!
I don't think they're in 1/2... 1/2 sucks. Just sin, cos, tan graphs I think and the circle.

That's right, 1/2 is rather boring
3/4 is better, but still boring :P
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