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anonymous
 5 years ago
How do I convert: y = 6 sqrt(2) sin(x)6 sqrt(2) cos(x)
into the form y = A sin(BxC) that has the same graph as the above?
WolframAlpha tells me I'm supposed to get: y = 12sin(pi/4  x)
But I want to know how I get there.
anonymous
 5 years ago
How do I convert: y = 6 sqrt(2) sin(x)6 sqrt(2) cos(x) into the form y = A sin(BxC) that has the same graph as the above? WolframAlpha tells me I'm supposed to get: y = 12sin(pi/4  x) But I want to know how I get there.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0im waiting for some one to respond to see how they figure this out!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Original Equation for better readability: \[y = 6 \sqrt(2) \sin(x)  6 \sqrt(2) \cos(x)\] And the equation in the \[y=A \sin(BxC)\] form: \[y = 12\sin(\pi/4  x)\] ....How do I get from original to final equation posted?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You want to put a sum of sine and cosine into one sine. You can consider the following:\[r \sin(x + \alpha) = r \cos \alpha \sin x + r \sin a \cos x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For the two expressions to be identical, you have to equate the coefficients on either side and solve for r and alpha.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Does this make sense?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So\[r \cos \alpha = 6 \sqrt{2}, r \sin \alpha = 6 \sqrt{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Divide sine by cosine to give\[\frac{r \sin \alpha}{r \sin \alpha}=\tan \alpha = 1 \rightarrow \alpha = \tan^{1}(1) = \frac{\pi}{4}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Substitute this into either one of the sine or cosine expressions to get r:\[r \cos \alpha = r \cos (\pi/4)=r \frac{1}{\sqrt{2}}=6 \sqrt{2} \rightarrow r = 12\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what is happenin here

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[6\sqrt{2}\sin x 6\sqrt{2} \cos x = 12\sin(x  \frac{\pi}{4})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh sweet, I think I can pick it up from here. Thanks so much!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Your Wolframalpha answer is the same  \[12\sin(x  \pi/4) = 12 \sin ((\pi/4 x))=12\sin (\pi/4x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh, btw, on the step where you're dividing sin by cos to get tan, why did you divide 2 sins? Is that just a typo or am I missing something?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no prob, thanks a ton man, it makes sense now.
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