Is there an equation for sinusoid about a curve?

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In summary, there is a function that can represent a sine wave with a curved center line. The function is r = a - b*cos(w*t), where a is the radius of the center circle, b is the amplitude of the sine wave, w is the frequency, and t is the angle. An example of this function can be seen in the provided image with a = 5, b = 0.5, and w = 10.
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corona7w
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The typical sine wave y = sin(x) has its center line as y = 0. Is there any equation I can represent a sine wave that has a center line as a curve? Something like the edge of the cookie cutter:
http://www.pmeartsandcrafts.com/4010-16826-large/round--wavy-edge-cutters-xxxl.jpg
 
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You basically need a sine wave along a curved dimension. Here is one function that achieves this.

r = a - b*cos(w*t)
a is the radius of center circle.
b is the amplitude of sine wave.
w is the frequency of the wave. I chose integer value for w to make sure the sine wave ends where it started.
t is the angle, goes from 0 to 2pi.

Here is an http://shareimage.org/images/uh7fobqbcznu724zhu.png" with a = 5, b = 0.5, w = 10.
 
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FAQ: Is there an equation for sinusoid about a curve?

1. What is a sinusoid curve?

A sinusoid curve is a mathematical function that represents a smooth oscillating pattern. It is a type of periodic function that repeats itself at regular intervals and can be described by the trigonometric function sine or cosine.

2. What is the equation for a sinusoid curve?

The general equation for a sinusoid curve is y = A sin(Bx + C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift. This equation can be modified to fit specific sinusoid curves by adjusting the values of A, B, C, and D.

3. How do you graph a sinusoid curve?

To graph a sinusoid curve, plot points using the general equation y = A sin(Bx + C) + D. The amplitude determines the vertical distance between the maximum and minimum points, the frequency determines the number of oscillations in a given interval, the phase shift determines the horizontal shift of the curve, and the vertical shift determines the overall position of the curve on the y-axis.

4. What is the period of a sinusoid curve?

The period of a sinusoid curve is the length of one complete cycle, which can be calculated by dividing 2π by the frequency (T = 2π/B). It represents the distance between two consecutive maximum or minimum points on the curve.

5. What are some real-life applications of sinusoid curves?

Sinusoid curves are used to model various natural phenomena, such as sound waves, light waves, and electromagnetic waves. They are also commonly used in fields such as physics, engineering, and economics to analyze and predict periodic patterns and oscillations.

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