Solve Equations of Curves - Get Help Now!

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In summary, the conversation discusses the use of polar coordinates to derive the equation of a curve described by a fixed point on a rolling circle. The stationary circle has a diameter of A and the rolling circle also has a diameter of A with its center located at (0,0). The coordinates of the given point can be determined using the angles \theta and \phi, which are related through right triangles.
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wilhelmsir
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[SOLVED] equations of curves

a circle of diameter A rolls without slipping along the outer circumference of a stationary circle of the same diameter. use polar coordinates to derive the equation of a curve described by some fixed point on the rolling circle. "can anyone help me out in this?"thanks 4 yo kindness
 
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Assume the stationary circle has center at (0, 0). Let [itex]\theta[/itex] be the angle the center of the rolling circle makes with the x-axis. Then the center of the rolling circle is distance 2A from the origin and has [itex]x= 2A cos(\theta)[/itex], [itex]y= 2A sin(\theta)[/itex] Now let [itex]\phi[/itex] be the angle the line from the center of the rolling circle to the given point. Then the given point has coordinates [itex]x= A cos(\phi)+ 2A sin(\theta)[/itex] and [itex]y= A sin(\phi)+ 2A sin(\theta)[/itex].

Of course, [itex]\theta[/itex] and [itex]\phi[/itex] are not independent. Draw a few pictures and right triangles to see how they are related. Then you can replace one by the other to get a single parameter.
 
  • #3
thanks a lot HallsofIvy
 

Related to Solve Equations of Curves - Get Help Now!

What is the process for solving equations of curves?

The process for solving equations of curves involves isolating the variable on one side of the equation and simplifying the other side. This can be done by using algebraic manipulations such as addition, subtraction, multiplication, and division, as well as applying the concept of inverse operations.

Can all curves be solved by equations?

Not all curves can be solved by equations. Some curves, such as fractals and chaotic curves, cannot be represented by a single equation. However, many common curves, such as lines, parabolas, and circles, can be solved by equations.

What are some common techniques for solving equations of curves?

Some common techniques for solving equations of curves include substitution, elimination, and graphing. These techniques involve manipulating the equations in different ways to isolate the variable and find its value.

What are the key factors to consider when solving equations of curves?

The key factors to consider when solving equations of curves include the type of curve, the degree of the equation, and the available tools and techniques. It is also important to carefully follow the order of operations and check for extraneous solutions.

Can I get help with solving equations of curves?

Yes, there are many resources available to help with solving equations of curves. You can seek assistance from a teacher or tutor, use online tutorials and practice problems, or consult textbooks and reference materials. Additionally, there are many software programs and calculators that can help with solving equations of curves.

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