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PreCalculus Lesson 17 – Tips on how to graph Polar Equations

When trying to graph polar equations, you will often have to put in (almost) every possible angle into your scientific calculator to find the radius for each angle. Then when you have all of the points (there are about 20) to graph.

The instruction manual does not use all 20 angles due to space constraints. Often students do not know the shape of the initial graph, and the only option is to graph each angle to determine the radius for each angle. This can be a long process.

A recommendation of a good scientific calculator makes this job a little easier. If you do not have a “textbook” scientific calculator (one that allows you to input the information as you see it in the Student Workbook), I recommend the free online scientific calculator at At the top of the page there is a drop down menu of “Math Tools”. Choose the scientific calculator. The following key settings are for use on desktop version, not the app.

To work 17A problem #9, you will want to input the data as follows.

For theta, you will simply put the 20 different angles possible.

Switch from DEG to RAD at the top of the calculator. Scientific calculators do not use reciprocal formulas. You will nee to rewrite 2𝑡𝑎𝑛(θ)𝑠𝑒𝑐(θ) as You will type out the words “tan”, “cos”, “pi”

To input a particular angle,

you will type:

This will give you the answer: 1.333
To change the angles, you will need to click on the angle and change the numbers accordingly.

If you choose the graphing feature of Desmos® (you will need to change calculator using the “Math Tools” dropdown), simply type the 𝑟 = before the equation below

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