Match each equation with its polar graph from choices A–D.
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Question

Match each equation with its polar graph from choices A–D.

r = cos 2θ

Accepted Answer

Welcome back, everyone. Grab the given polar equation. R equals 63 theta. We're given our coordinate plane and essentially we want to evaluate R or theta values that are multiples of pi divided by 12. So first of all, we begin with 0. If we substitute 0 into the given function, we're going to get 0, right? So our first value is 0. For the second one, we're actually going to write them down, right, and then we are going to add those points. So for the first one it's 0. for pi divided by 12, if we subsue that for the, we're going to get about 4.2. For pi divided by 6, which is essentially 2 pi divided by 12, right? We're going to get 6 followed by. I divided by 4. This is where we are going to get approximately 4.2 game or pi divided by we, we are going to get 0 or 5 pi divided by 12, we're going to get approximately 4.2, or pi divided by 2, we are going to get -6. 7 pi divided by 12, we're going to get approximately. 4.2 or 2 divided by 3, we are going to get 0. We pi divided by 4 we're going to get approximately 4.2 5 pi divided by 6. For this one we're going to get 6, 11 pi divided by 12, we're going to get approximately 4.2. Now for the value of pi, we're going to get 0. We 13 divided by 12, for this one we're going to get about -4.2. 7 pi divided by 6 for this value we're going to get approximate we're we're actually going to get exactly -6. 5 pi divided by 4. For this one we're going to get. -4.2, approximately, right? Now 4 divided by 3 for this value, we're going to get 0. Followed by 17 pi divided by 12 for this value we're going to get approximately. 4.2. Now for 3 divided by 2, we're going to get 6 followed by 19 pi divided by 12 for this value we get approximately 4.2. 55 divided by 3 for this value, we are going to get 0. 7 pi divided by 4. This is where we get approximately -4.2, 11 pi divided by 6. This is where we get -6, 23 pi divided by 12 for this value we get approximately 4.2, and for 2 by once again, we get 0. So now let's add those values. First of all, we get 0 at 0. I divided by 12 gives us about 4.2. So let's identify approximately 4.2. Well then we have our point. Now, we want to add a value of 6. Then we want to add a value of about 4 points to a gain. So essentially we have 4 and then we want to add approximately 4.2, right? So we have 0 at I divided by 3. 55 divided by 12 gives us approximately -4.2. So since it is a negative value, we want to look at the opposite quadrant, and we want to add a value of approximately -4.2. Well done. Then we have 6 for pi divided by 2. Then we have 4.2, approximately -4.2. Then we have 0 followed by 4.2. And 3 by divided by 4. So we have 3 by divided by 4, and now we need a value of approximately 4.2. Followed by 6 at 55 divided by 6. So we need a value of 6. Followed by approximately 4.2. Well done, then we have 0, and then once again we have approximately 4.2 at 13 pi divided by 12, right? So now we want to extend. And identify -4.2, this is the same point, right? So, essentially since we encountered the same point, we can ignore it, followed by negative. 64 7 pi divided by 6. Once again we encountered the same point, negative 4.2. This is the point that we have, 0, 4.2 adds 17 pi divided by 12. So for this one, we also already have that point and now if we move on, we will notice that we have all of these points. So we basically get a flower graph with three petals. So let's connect those points. So we have our first pan, followed by the 2nd 1. And finally, the 3rd 1. And that's how we expect our graph to look like. Thank you for watching.

Match each equation with its polar graph from choices A–D.
r = cos 2θ

Key Concepts

Polar Coordinates and Graphs

Rose Curves and Their Properties

Symmetry in Polar Graphs

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