In Exercises 1–10, indicate if the point with the given polar coo...

Question

In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph.

(3, −135°)

Accepted Answer

Hello, today we're going to be identifying the position of the given polar coordinate. So what we are given is two comma negative degrees. Now, one thing to note about polar coordinates is that the general form of a polar coordinate is given to us as R comma theta. Here R represents the radius of the polar coordinate and theta represents the angle of the polar coordinate. So if we want to find the position of our polar coordinate, we're first going to need to identify the radius. Now two is in the position of R. So that means the radius of the polar coordinate is equal to two. If we take a look at the polar axis, notice that the polar axis is made up of multiple circles, the innermost circle is a circle of radius one followed by a circle of radius two, followed by a circle of radius three and followed by a circle of radius four. Since we know that the radius of the given polar coordinate is the radius of positive two, that means the starting position is going to be at the circle of radius two in the positive direction. Now we need to identify our angle theta. Now, theta is given to us as negative 45 degrees. What this means is that we're going to want to travel 45 degrees in the negative direction. Now, normally, when we are traveling along the unit circle, the positive direction is going to be the counter clockwise direction. But if we want to travel the negative direction, we'll have to travel in the clockwise direction. That means that starting at radius two on the polar axis, we're going to have to travel 45 degrees in the negative direction. And that is going to put us at the position R. What this means is that the polar coordinate two comma negative is located at position R. And with that being said, the answer to this problem is going to be C so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (3, −135°)