# Rearranging a general sine function

• Nov 29th 2009, 02:35 AM
maybealways
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.
• Nov 29th 2009, 03:43 AM
e^(i*pi)
Quote:

Originally Posted by maybealways
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 $y=Asin[B(x+C)]$
• Nov 29th 2009, 04:06 AM
maybealways
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 $
y=A sin B (x-C)+D
$
, what would I need to do?
• Nov 29th 2009, 05:37 AM
HallsofIvy
Quote:

Originally Posted by maybealways
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 $
y=A sin B (x-C)+D
$
, 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.