How To Plot Polar Coordinates In Desmos?

How to Plot Polar Coordinates in Desmos

Polar coordinates are a way of representing a point in a plane using two numbers: the radius, which is the distance from the origin to the point, and the angle, which is the angle between the positive x-axis and the line from the origin to the point. Polar coordinates are often used in mathematics and physics to represent curves and surfaces.

In this article, we will show you how to plot polar coordinates in Desmos, a free online graphing calculator. We will start by explaining what polar coordinates are and how they are represented in Desmos. Then, we will show you how to plot a few different types of polar curves, including circles, spirals, and cardioids.

By the end of this article, you will be able to use Desmos to plot polar coordinates and create beautiful graphs of polar curves.

What are Polar Coordinates?

Polar coordinates are a way of representing a point in a plane using two numbers: the radius, which is the distance from the origin to the point, and the angle, which is the angle between the positive x-axis and the line from the origin to the point.

The radius is represented by the symbol r, and the angle is represented by the symbol . The point with radius r and angle is written as (r, ).

For example, the point with radius 5 and angle 45 is written as (5, 45). This point is located 5 units from the origin on the line that makes an angle of 45 with the positive x-axis.

How to Plot Polar Coordinates in Desmos

To plot a point in polar coordinates in Desmos, you can use the following syntax:

“`
plot(r, )
“`

where r is the radius and is the angle.

For example, to plot the point with radius 5 and angle 45, you would use the following command:

“`
plot(5, 45)
“`

This will create a point at the following coordinates:

“`
(5, cos(45), sin(45))
“`

Plotting Polar Curves

In addition to plotting individual points, you can also use polar coordinates to plot curves. To do this, you can use the following syntax:

“`
plot(r())
“`

where r() is a function of the angle .

For example, to plot the circle with radius 5, you would use the following command:

“`
plot(5 * cos(), 5 * sin())
“`

This will create a circle with the following equation:

“`
x^2 + y^2 = 25
“`

You can also use polar coordinates to plot spirals, cardioids, and other types of curves. For more information, please see the Desmos documentation.

“`html

Step	Instructions	Example
1	Enter the equation of the polar curve in the Desmos search bar.	r = 2sin()
2	Click the “Plot” button.
3	To change the range of theta, use the sliders in the upper right corner of the graph.

“`

What are polar coordinates?

Polar coordinates are a way of representing a point in a plane using two numbers: the r-coordinate, which is the distance from the origin, and the -coordinate, which is the angle from the positive x-axis.

To plot a point in polar coordinates, you first need to find its r– and -coordinates. The r-coordinate is simply the distance from the origin to the point. To find the -coordinate, you need to draw a line from the origin to the point, and then measure the angle between that line and the positive x-axis.

Once you have the r– and -coordinates of a point, you can plot it on a polar graph by drawing a circle with the origin as its center and the radius equal to the r-coordinate. Then, draw a line from the origin to the point, and mark the angle from the positive x-axis as the -coordinate.

Here is an example of a polar graph:

As you can see, the graph of y = sin x in polar coordinates is a circle. The r-coordinate of each point on the graph is equal to the sine of the -coordinate.

Polar coordinates are often used to represent curves that are not lines. For example, the graph of r = sin is a cardioid, and the graph of r = cos is a limaon.

Polar coordinates can also be used to represent functions. For example, the function f() = sin is a spiral.

How to plot polar coordinates in Desmos?

Plotting polar coordinates in Desmos is very easy. To do this, simply follow these steps:

1. Click on the + button in the top left corner of the Desmos window.
2. Select the Polar option.
3. Enter the r– and -coordinates of the point you want to plot.
4. Click on the Enter button.

The point will be plotted on the polar graph.

You can also plot multiple points by entering them in a list. For example, to plot the points (1, /2), (2, ), and (3, 3/2), you would enter the following into the Desmos window:

“`
[1, /2, 2, , 3, 3/2]
“`

The points will be plotted in order from left to right.

You can also plot curves in polar coordinates by entering a function. For example, to plot the curve r = sin , you would enter the following into the Desmos window:

“`
r = sin()
“`

The curve will be plotted on the polar graph.

Plotting polar coordinates in Desmos is a great way to visualize curves and functions. It is also a very easy way to graph equations that are not in Cartesian coordinates.

How To Plot Polar Coordinates In Desmos?

Polar coordinates are a way of representing a point in a plane using two numbers: the r-coordinate, which is the distance from the origin, and the -coordinate, which is the angle from the positive x-axis. To plot a point in polar coordinates, you can use the following steps:

1. Open the Desmos graphing calculator.
2. Click on the “+” button to add a new function.
3. In the “Function” field, type the following:

“`
polar(r, )
“`

where `r` is the r-coordinate of the point and “ is the -coordinate.
4. Click on the “Graph” button to see the point plotted on the graph.

You can also plot multiple points in polar coordinates by using the following steps:

1. Open the Desmos graphing calculator.
2. Click on the “+” button to add a new function.
3. In the “Function” field, type the following:

“`
polar(r1, 1) + polar(r2, 2) + … + polar(rn, n)
“`

where `r1`, `1`, `r2`, `2`, …, `rn`, and `n` are the r– and -coordinates of the points you want to plot.
4. Click on the “Graph” button to see the points plotted on the graph.

Examples of Polar Coordinates Graphs

Here are some examples of polar coordinates graphs:

• A circle with radius 1 is represented by the equation `polar(1, )`.
• A line with slope `m` and y-intercept `b` is represented by the equation `polar(m * + b, )`.
• A parabola with vertex at the origin and focal length `f` is represented by the equation `polar(r = f * cos(2))`.
• An ellipse with center at the origin, semi-major axis `a`, and semi-minor axis `b` is represented by the equation `polar(r = a * cos() + b * sin())`.

Tips for Plotting Polar Coordinates in Desmos

Here are some tips for plotting polar coordinates in Desmos:

• To plot a point, you can use the following steps:

1. Open the Desmos graphing calculator.
2. Click on the “+” button to add a new function.
3. In the “Function” field, type the following:

“`
polar(r, )
“`

where `r` is the r-coordinate of the point and “ is the -coordinate.
4. Click on the “Graph” button to see the point plotted on the graph.

• To plot multiple points, you can use the following steps:

1. Open the Desmos graphing calculator.
2. Click on the “+” button to add a new function.
3. In the “Function” field, type the following:

“`
polar(r1, 1) + polar(r2, 2) + … + polar(rn, n)
“`

where `r1`, `1`, `r2`, `2`, …, `rn`, and `n` are the r– and -coordinates of the points you want to plot.
4. Click on the “Graph” button to see the points plotted on the graph.

• To change the color of a point, you can use the following steps:

1. Right-click on the point.
2. Select “Properties” from the menu.
3. In the “Color” field, select the color you want.

• To change the size of a point, you can use the following steps:

1. Right-click on the point.
2. Select “Properties” from the menu.
3. In the “Size” field, enter the size you want.

• To add a label to a point, you can use the following steps:

1. Right-click on the point.
2. Select **”Properties”

How do I plot polar coordinates in Desmos?

To plot polar coordinates in Desmos, follow these steps:

1. Click the +” button in the top left corner of the Desmos window.
2. Select Equation from the menu that appears.
3. In the Equation window, type the following:

“`
polar(r, theta)
“`

where `r` is the radius of the polar coordinate and `theta` is the angle of the polar coordinate.
4. Click the Graph button to see the polar coordinate plotted on the graph.

What are the different parts of a polar coordinate?

The different parts of a polar coordinate are the radius and the angle. The radius is the distance from the origin to the point, and the angle is the angle that the line from the origin to the point makes with the positive x-axis.

How do I convert Cartesian coordinates to polar coordinates?

To convert Cartesian coordinates to polar coordinates, use the following formulas:

“`
r = \sqrt{x^2 + y^2}
\theta = \tan^{-1}{\frac{y}{x}}
“`

where `r` is the radius of the polar coordinate, `theta` is the angle of the polar coordinate, `x` is the x-coordinate of the Cartesian coordinate, and `y` is the y-coordinate of the Cartesian coordinate.

How do I convert polar coordinates to Cartesian coordinates?

To convert polar coordinates to Cartesian coordinates, use the following formulas:

“`
x = r \cos{\theta}
y = r \sin{\theta}
“`

where `x` is the x-coordinate of the Cartesian coordinate, `y` is the y-coordinate of the Cartesian coordinate, `r` is the radius of the polar coordinate, and `theta` is the angle of the polar coordinate.

What are some applications of polar coordinates?

Polar coordinates are used in a variety of applications, including:

• Geometry
• Trigonometry
• Physics
• Engineering
• Astronomy

Where can I learn more about polar coordinates?

There are a number of resources available to learn more about polar coordinates, including:

• Online tutorials
• Textbooks
• Reference books
• Math websites
• Math forums

Is there anything else I should know about polar coordinates?

Polar coordinates are a useful tool for representing points in a plane. However, it is important to note that polar coordinates are not as widely used as Cartesian coordinates. Therefore, it is important to be familiar with both types of coordinates.

In this blog post, we have discussed how to plot polar coordinates in Desmos. We first introduced the concept of polar coordinates and then showed how to plot them using the Desmos graphing calculator. We also provided several examples of polar graphs, including circles, ellipses, and spirals. Finally, we discussed some of the advantages and disadvantages of using polar coordinates.

We hope that this blog post has been helpful in learning how to plot polar coordinates in Desmos. If you have any questions or comments, please feel free to leave them below.