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

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May 22, 2024
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I have made a formula for a sine wave with aa amplitude, pp phase shift and ww wavelength, where aa and ww are measured in units and pp is measured in degrees. Here it is:
asin(π(180x+wp)180w)a\sin\left(\frac{\pi(180x+wp)}{180w}\right)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! =]
 
improvement that can be made for it to be computable in less steps to someone else
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.

180x+wp180w\displaystyle \frac{180x+wp}{180w}

:)
 
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.

180x+wp180w\displaystyle \frac{180x+wp}{180w}

:)
If I decompose it into more ratios, it means there will be extra steps: an addition.
 
If I decompose it into more ratios, it means there will be extra steps: an addition.
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:

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

π1.5+725\displaystyle \frac{\pi}{1.5}+\frac{7}{25}

:)
 
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:

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

π1.5+725\displaystyle \frac{\pi}{1.5}+\frac{7}{25}

:)

π(180x+wp180w)\pi\left(\frac{180x+wp}{180w}\right)π(180x180w+wp180w)\pi\left(\frac{180x}{180w}+\frac{wp}{180w}\right)π(xw+p180)\pi\left(\frac{x}{w}+\frac{p}{180}\right)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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