How To Graph Polar Coordinates On Ti-84?

How to Graph Polar Coordinates on the TI-84 Plus Calculator

Polar coordinates are a useful way to represent points in a plane. They are often used in physics and engineering, as well as in mathematics. In this tutorial, we will show you how to graph polar coordinates on the TI-84 Plus calculator.

We will start by discussing what polar coordinates are and how to convert between rectangular and polar coordinates. Then, we will show you how to graph polar equations on the TI-84 Plus calculator. Finally, we will give you some practice problems to test your understanding.

By the end of this tutorial, you will be able to graph polar coordinates on the TI-84 Plus calculator with ease.

Step	Explanation	Screenshot
1. Press MODE and select POLAR.	This will change the calculator’s mode to polar coordinates.
2. Enter the r and values of your point.	The r value is the distance from the origin, and the value is the angle from the positive x-axis.
3. Press GRAPH to graph your point.	Your point will be plotted on the polar graph.

Entering Polar Coordinates

To enter a point in polar coordinates, you can use the following steps:

1. Press the MODE button.
2. Use the arrow keys to scroll to the POLAR option.
3. Press the ENTER button.
4. Enter the r-coordinate of the point.
5. Press the , (comma) key.
6. Enter the -coordinate of the point.
7. Press the ENTER button.

The point will be plotted on the polar graph.

Example: To plot the point (3, 45), you would follow these steps:

1. Press the MODE button.
2. Use the arrow keys to scroll to the POLAR option.
3. Press the ENTER button.
4. Enter 3.
5. Press the , (comma) key.
6. Enter 45.
7. Press the ENTER button.

The point (3, 45) will be plotted on the polar graph.

Changing the Mode of the Calculator to Polar Coordinates

To change the mode of the calculator to polar coordinates, you can use the following steps:

1. Press the MODE button.
2. Use the arrow keys to scroll to the POLAR option.
3. Press the ENTER button.

The calculator will now be in polar coordinates mode.

Plotting a Polar Graph

To plot a polar graph, you can use the following steps:

1. Enter the equation of the polar graph.
2. Press the GRAPH button.

The polar graph will be plotted on the screen.

Example: To plot the polar graph of r = 3sin(), you would follow these steps:

1. Enter 3sin().
2. Press the GRAPH button.

The polar graph of r = 3sin() will be plotted on the screen.

Changing the Appearance of Polar Graphs

You can change the appearance of polar graphs by changing the following settings:

• Axes: You can change the axes of the polar graph by pressing the MODE button and selecting the desired option.
• Gridlines: You can change the gridlines of the polar graph by pressing the ZOOM button and selecting the desired option.
• Labels: You can add labels to the polar graph by pressing the WINDOW button and entering the desired text.

Example: To change the axes of the polar graph to logarithmic, you would follow these steps:

1. Press the MODE button.
2. Use the arrow keys to scroll to the POLAR option.
3. Press the ENTER button.
4. Use the arrow keys to scroll to the LOG option.
5. Press the ENTER button.

The axes of the polar graph will now be logarithmic.

Polar coordinates can be used to graph a variety of different functions. By understanding how to enter polar coordinates, change the mode of the calculator to polar coordinates, and plot a polar graph, you can easily create and visualize polar graphs.

Solving Equations in Polar Coordinates

Polar coordinates can be used to solve equations in a variety of ways. In this section, we will discuss three methods for solving equations in polar coordinates:

• Graphing the equation: The first method is to graph the equation and then find the points where the graph intersects the polar axis. These points are the solutions to the equation.
• Using the polar form of the equation: The second method is to use the polar form of the equation to solve for r. Once you have found r, you can use the conversion formula to find the corresponding x- and y-coordinates.
• Using the parametric form of the equation: The third method is to use the parametric form of the equation to solve for t. Once you have found t, you can use the conversion formula to find the corresponding x- and y-coordinates.

We will now illustrate each of these methods with an example.

Example: Solve the equation r = 2 sin() for .

• Graphing the equation: We can graph the equation r = 2 sin() by plotting the points (r, ) for various values of . We can do this using a graphing calculator or a computer program. The graph of the equation is shown below.

The graph of the equation intersects the polar axis at the points (1, 0) and (-1, 0). These are the solutions to the equation.

• Using the polar form of the equation: We can also solve the equation r = 2 sin() by using the polar form of the equation. The polar form of the equation is r = 2 sin(). To solve this equation for r, we can use the following steps:

1. Isolate r on the left-hand side of the equation.
2. Divide both sides of the equation by 2.
3. Take the inverse sine of both sides of the equation.

This gives us the following solution:

= arcsin(r / 2)

• Using the parametric form of the equation: We can also solve the equation r = 2 sin() by using the parametric form of the equation. The parametric form of the equation is x = r cos() and y = r sin(). To solve this equation for , we can use the following steps:

1. Set x equal to 0.
2. Solve for .

This gives us the following solution:

= / 2

We can also solve for by setting y equal to 0. This gives us the following solution:

= 3 / 2

Therefore, the solutions to the equation r = 2 sin() are = / 2 and = 3 / 2.

Finding the Intersection of Two Polar Graphs

The intersection of two polar graphs can be found by using the following steps:

1. Graph the two polar graphs on the same coordinate system.
2. Find the points where the two graphs intersect.
3. Use the conversion formula to find the corresponding x- and y-coordinates of the intersection points.

We will now illustrate this process with an example.

Example: Find the intersection of the polar graphs r = 1 and r = 2 sin().

• Graph the two polar graphs: We can graph the two polar graphs by plotting the points (r, ) for various values of . We can do this using a graphing calculator or a computer program. The graphs of the two polar graphs are shown below.

* **Find the points where the two graphs intersect:** The two graphs intersect at the points (1, 0) and (2, / 2).

* **Use the conversion formula to find the corresponding x- and y-coordinates of the intersection points:** The conversion formula is x = r cos() and y = r sin(). Using this formula, we can find the corresponding x- and y-coordinates of the intersection points as follows:

(1, 0) -> (1, 0)
(2, / 2) -> (0, 2

How do I graph polar coordinates on a TI-84?

1. Press the MODE button and select POLAR.
2. Enter the r-value and -value of the point you want to graph.
3. Press the GRAPH button.

The point will be plotted on the polar graph.

How do I change the range of the polar graph?

1. Press the WINDOW button.
2. Use the XMIN, XMAX, YMIN, and YMAX sliders to adjust the range of the graph.
3. Press the GRAPH button to see the changes.

How do I add labels to a polar graph?

1. Press the 2nd GRAPH button.
2. Select the LABEL option.
3. Enter the x– and y-values of the points you want to label.
4. Press the ENTER button.

The labels will be added to the graph.

How do I save a polar graph?

1. Press the 2nd GRAPH button.
2. Select the SAVE option.
3. Enter a name for the graph.
4. Press the ENTER button.

The graph will be saved to your calculator.

How do I recall a saved polar graph?

1. Press the 2nd GRAPH button.
2. Select the RECALL option.
3. Enter the name of the graph you want to recall.
4. Press the ENTER button.

The graph will be recalled on the calculator.

In this tutorial, we have learned how to graph polar coordinates on the TI-84 Plus CE graphing calculator. We first learned how to enter polar coordinates in the MODE menu. Then, we learned how to graph polar equations using the GRAPH menu. Finally, we learned how to use the TRACE feature to explore polar graphs.

We can summarize the main points of this tutorial as follows:

• To enter polar coordinates in the MODE menu, press MODE and select POLAR.
• To graph a polar equation using the GRAPH menu, press Y= and enter the equation in the form r = f().
• To use the TRACE feature to explore a polar graph, press TRACE and use the arrow keys to move the cursor along the graph.

We hope that this tutorial has been helpful. Please feel free to leave any questions or comments below.