How do I convert the equation y = x^(2) to polar coordinates?

In summary, to convert y = x^2 to an equation in polar coordinates, you can use the identities x = rcos(theta) and y = rsin(theta) and the equation tan(theta) = y/x to get sin(theta) = rcos^2(theta).
  • #1
stau40
37
0

Homework Statement


Convert to an equation in polar coordinates y = x^(2)


Homework Equations


x = r cos (theta) , y = r sin (theta) , tan (theta) = y/x


The Attempt at a Solution


Here is my work so far: y=x^(2) so r sin (theta) = (r cos (theta))^2 and r sin (theta) = r^(2) cos^(2) theta. I'm not sure how to move the r's to one side of the equation though. Can I apply tan (theta) = y/x or ? Thanks in advance!
 
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  • #2
stau40 said:

Homework Statement


Convert to an equation in polar coordinates y = x^(2)


Homework Equations


x = r cos (theta) , y = r sin (theta) , tan (theta) = y/x


The Attempt at a Solution


Here is my work so far: y=x^(2) so r sin (theta) = (r cos (theta))^2 and r sin (theta) = r^(2) cos^(2) theta. I'm not sure how to move the r's to one side of the equation though. Can I apply tan (theta) = y/x or ? Thanks in advance!
You can divide both sides of your equation by r to get sin(theta) = rcos^2(theta). It's not always legitimate to do this, as you might be losing solutions for r = 0. In this case, r = 0 is still a solution.
 

FAQ: How do I convert the equation y = x^(2) to polar coordinates?

1. What are polar coordinates?

Polar coordinates are a coordinate system used to locate points in a two-dimensional plane. They use a distance (r) and an angle (θ) from a fixed point, typically the origin, to describe the location of a point.

2. How are polar coordinates different from Cartesian coordinates?

Polar coordinates use a distance and angle to describe a point, while Cartesian coordinates use x and y coordinates. Polar coordinates are better suited for describing circular or radial patterns, while Cartesian coordinates are better for describing linear patterns.

3. How do you convert between polar and Cartesian coordinates?

To convert from polar coordinates to Cartesian coordinates, you can use the following formulas: x = r * cos(θ) and y = r * sin(θ). To convert from Cartesian coordinates to polar coordinates, you can use the formulas: r = √(x^2 + y^2) and θ = tan^-1 (y/x).

4. What are some real-world applications of polar coordinates?

Polar coordinates are commonly used in physics, engineering, and navigation. They are useful for describing circular motion, such as the path of a satellite orbiting the Earth. They are also used in polar graphs to plot data points, such as temperature changes over time.

5. Can polar coordinates be used in three-dimensional space?

No, polar coordinates are only used in two-dimensional space. In three-dimensional space, we use spherical coordinates, which include a third coordinate, ϕ, to describe the angle from the polar axis.

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