In Exercises 35–44, test for symmetry and then graph each pola...

Question

In Exercises 35–44, test for symmetry and then graph each polar equation. r = 1 / 1−cos θ

Accepted Answer

Test the polar equation for symmetry and sketch its graph where we have R equals three divided by three minus cosine data. And we're also given a polar coordinate system to graph our equation on now to graph this, we need to check three different symmetry types. You have polar symmetry, polar symmetry and line of data equals pi divided by two symmetry. Now to check our first symmetry, we need to use of substitution. Let's substitute data with negative data. We will get far is equals to three divided by three minus cosine of negative data. Now cosine we know isn't even function. This means if we have cosine of a negative value such as an X, this is the same as cosine of the positive X. So we can just replace our negative angle with positive angle giving us three minus cosine of data. This equation is the same as our original. So we confirm we do have polar symmetry. Now we can check our line symmetry over A theta equals pi divided by two. For this, we will replace both our radius and our data with negative values negative R is equals to three divided by three minus cosine of negative data. By our previous, we know at the bottom of our fraction goes back to three minus cosine theta. Finally divided by negative one gives us R equals negative three divided by three minus cosine theta. This is not the same as the original. So we cannot confirm if there is symmetry over this line. Finally, let's check our pulse symmetry. You have negative R equals three divided by three minus cosine data which gives us R equals negative three divided by three minus cosine data. This is not the same as our original. So we cannot confirm Pole symmetry either. Now that we have all of our symmetries, we can go ahead and graph our function. No, I have a table of values here which we can use to graph chose some values from zero the pi and we can plot these on the graph by moving our radius in the direction of our angle data. In other words, this first point is 01.5 in the direction of zero from the origin. We'll move to the right by 1. which is roughly at this point on the graph. Our next one will be pi divided by six and 1. pi divided by 31.2 pi divided by 21, two pi divided by 30. five pi divided by 60.8 NP 0.75. Now we also confirm Polar Symmetry which means this will be reflected vertically, which means we draw a curve through all of our points and then reflect it vertically, which gives us a graph that looks like this. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 35–44, test for symmetry and then graph each polar equation. r = 1 / 1−cos θ

Key Concepts

Polar Coordinates and Polar Equations

Symmetry Tests in Polar Graphs

Handling and Simplifying Rational Polar Equations

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