Found a sine formula: a sin( (pi(180x + wp))/(180w) )

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erikthemathematician

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I have made a formula for a sine wave with [imath]a[/imath] amplitude, [imath]p[/imath] phase shift and [imath]w[/imath] wavelength, where [imath]a[/imath] and [imath]w[/imath] are measured in units and [imath]p[/imath] is measured in degrees. Here it is:
[math]a\sin\left(\frac{\pi(180x+wp)}{180w}\right)[/math]I do not need this in any form, but I just wanted to know if there is any improvement that can be made for it to be computable in less steps to someone else. Any suggestions are welcome! =]
 
erikthemathematician said:
improvement that can be made for it to be computable in less steps to someone else
Click to expand...
The input to the sine function can be changed. Decompose the following expression into a sum of two ratios and then cancel common factors in each.

\(\displaystyle \frac{180x+wp}{180w}\)

:)
 
Otis said:
The input to the sine function can be changed. Decompose the following expression into a sum of two ratios and then cancel common factors in each.

\(\displaystyle \frac{180x+wp}{180w}\)

:)
Click to expand...
If I decompose it into more ratios, it means there will be extra steps: an addition.
 
erikthemathematician said:
If I decompose it into more ratios, it means there will be extra steps: an addition.
Click to expand...
Hi Erik. Please post your attempt, so we can see what you did. The simplified expression will contain one addition, just like your original expression. Here's an example:

\(\displaystyle \frac{25\pi+(1.5)(7)}{(25)(1.5)}\)

\(\displaystyle \frac{\pi}{1.5}+\frac{7}{25}\)

:)
 
Otis said:
Hi Erik. Please post your attempt, so we can see what you did. The simplified expression will contain one addition, just like your original expression. Here's an example:

\(\displaystyle \frac{25\pi+(1.5)(7)}{(25)(1.5)}\)

\(\displaystyle \frac{\pi}{1.5}+\frac{7}{25}\)

:)
Click to expand...

[math]\pi\left(\frac{180x+wp}{180w}\right)[/math][math]\pi\left(\frac{180x}{180w}+\frac{wp}{180w}\right)[/math][math]\pi\left(\frac{x}{w}+\frac{p}{180}\right)[/math]The reason I do not want to do this is because it has now 2 divisions and an addition.
 
Very well. Leave the factor as it is: 3 multiplications, 1 addition and 1 division.

:)
 
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