Modified Sine

I'm trying to create an excel sheet that will use the modified sine equation above to output a 360° displacement chart when a user types in the acceleration, velocity, total distance traveled and start and stop angles. From what I've been told previously this is the equation I have to use, but my background is more on the excel side of things so I'm having trouble understanding exactly how to break this equation down into something I can use.

Could someone please explain how to solve this equation using the variables that will be available that I described above? Does this equation require any more or any less variables than what will be available?

  • $\begingroup$ Just inspecting your equations, you have a parametric form of a plot. You can run these equations over any range of theta from 0 to Beta. You must include the parameter h or y in order to get a solution. Just shooting from the hip here but if you set Beta = 360 deg and use 3 nested if statements in excel I don't see any problem with plotting Theta vs. y. $\endgroup$
    – ShadowMan
    Sep 25, 2019 at 23:47

1 Answer 1


You can define the h and beta constants, either in a cell or as a defined name. After that, you can create a column with the theta parameter and another column with the calculated y parameter.

The formula for the y should use the IF and AND functions. Suppose the theta parameters are on column A. The formula should be something like

=IF(AND(0<=A1,A1<beta/8),h*(PI()/(4+PI()))*A1/beta - 1/4/(4+PI())*SIN(4*PI()*A1/beta),IF(AND(beta/8<=A1,A1<7*beta/8),h*(2*/(4+PI()))+PI()/(4+PI()))*A1/beta - 9/4/(4+PI())*SIN(4*PI()*A1/3/beta),h*(4/(4+PI()))+PI()/(4+PI()))*A1/beta - 1/4/(4+PI())*SIN(4*PI()*A1/beta) ) )

To break down the formula, the IFs statements define which equation to use. The criteria is accessed with the AND function, since you have a range on beta. The equation itself is straightforward.


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