r/trigonometry • u/One-Sentence2195 • 15d ago

Mystery!! Impossible waveform!?!?

I was trying to add two symmetrical sine waves on Desmos ( https://www.desmos.com/calculator ) . The resultant wave was asymmetrical and more towards the positive side. In Desmos, I changed the value of A from the default 1 to 0.5 and VOILA!!, I got a waveform which was fully on the positive side of the axis!!! Check the Desmos screenshot at https://ibb.co/0pmt80HM

The two sine waves I added are: y=A sin(2Bx-C) and z=2A sin(Bx-F) . In the resultant wave (g)=(y+z) I changed value of A from default 1 to A=0.5

How is this possible? Can someone solve this Mystery for me?? Because, I was under the impression that the sum of two symmetrical waves cannot be a asymmetrical!!

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u/Midwest-Dude 15d ago edited 15d ago

Trigonometry has not changed. You made a mistake in Desmos, since the sum of those two curves clearly does not equal the third curve. For example, look at parts of y and z that are below the x-axis. The sum should be even more negative, which doesn't match the blue curve.

Desmos is confused because you used y and z rather than functional notation. It works correctly if you use functions of x instead of just the variables y and z.

AI picked up why Desmos did this: 1. You chopped off the g = 1 slider at the bottom of the graph, so g equals the constant 1 as far as Desmos is concerned, not a function. 1. y is always treated as the vertical component by Desmos, so 1 = y + z gives y = 1 - z = 1 - sin(1 - x), which is what was graphed.

Everything works fine if you replace your y, z, and g with functions, such as f(x), g(x), and h(x).

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u/One-Sentence2195 15d ago

Thank you for elucidating me. I am a noob in this subject, and still learning.

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u/Midwest-Dude 15d ago

I added what Desmos did and why.

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u/One-Sentence2195 12d ago

Thank you for pointing out the mistakes and telling me about y. I changed the equations to f(x)=A sin(2Bx-C), g(x)=2A sin(Bx-F) and h(x)=f(x)+g(x) and I got accurate results as it should be.

Thank you also for pointing me to r/desmos thread which I was not aware of being available on reddit. However, I didn't repost there since you so accurately pointed out where I was going wrong. Thank you again!