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Math Help - Rearranging a general sine function

  1. #1
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    Rearranging a general sine function

    I feel annoyed because I can't rearrange something like this... ^^;;e

    Anyway, how do I rearrange this:
    y=A sin (Bx+C)+D

    into....

    y=A sin B (x-C)+D

    Can you please list the steps for me?

    Thanks.
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  2. #2
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    Quote Originally Posted by maybealways View Post
    I feel annoyed because I can't rearrange something like this... ^^;;e

    Anyway, how do I rearrange this:
    y=A sin (Bx+C)+D

    into....

    y=A sin B (x-C)+D

    Can you please list the steps for me?

    Thanks.
    This will only work if B \neq 0

    Consider the function Bx+k. We can take out a factor of B (because it's non-zero to give)

    B\left(x+\frac{k}{B}\right)

    Let C = \frac{k}{B} to give B(x+C)

    Therefore putting this new expression in place of the old one gives y=Asin[B(x+C)]
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  3. #3
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    Thank you, that helps a lot.

    But for the equation you arrived at, y=Asin[B(x+C)], why is the sign in the bracket an addition sign? Shouldn't it be a subtraction sign?


    So, if I wanted to rearrange this: y=3.123 sin (0.2178x-2.731)+18.43 into the <br />
y=A sin B (x-C)+D<br />
, what would I need to do?
    Last edited by maybealways; November 29th 2009 at 03:17 AM.
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  4. #4
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    Quote Originally Posted by maybealways View Post
    Thank you, that helps a lot.

    But for the equation you arrived at, y=Asin[B(x+C)], why is the sign in the bracket an addition sign? Shouldn't it be a subtraction sign?


    So, if I wanted to rearrange this: y=3.123 sin (0.2178x-2.731)+18.43 into the <br />
y=A sin B (x-C)+D<br />
, what would I need to do?
    ?? You said before that you wanted to take the "B" outside the sine function.

    Apparently, you just want to write 0.2178x- 2.731 as B(x- C). You can do that by "factoring out" 0.2178. 0.2178x- 2.731= 0.2178(x- 2.731/0.2718)= 0.2178(x- 10.04783) so "3.123 sin (0.2178x-2.731)+18.43= 3.123 sin(0.2178(x- 10.0483)+ 18.43.

    That is "A sin B(x- C)+ D" with A= 3.123, B= 0.2178, C= 10.0483, and D= 18.43.
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