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, 5π/4)

Accepted Answer

Hello, today we're going to be identifying the position of the given polar coordinate. So what we are given is negative four comma five pi over four. Now, one thing to note about the polar coordinate is that the general form of a polar coordinate is given to us as our comma theta R represents the radius of the polar coordinate and theta represents the angle of the polar coordinate. Now, in order to find the position of the given polar coordinate, let's start by identifying the radius, we can use the radius as the starting position for the polar coordinate. And in this case here, the radius is given to us as negative four. What this means is that the polar coordinate is going to have a release of four but in a negative direction. So let's find the starting position on the polar axis. Now notice that the polar axis is made up of multiple circles. The innermost circle represents 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 starting position is a radius of negative four. What this means is that the starting position of the polar coordinate is going to be four but in the negative direction. So it's going to be here between the 2nd and 3rd quadrant of the unit circle. Now let's identify our angle theta. Now the is given to us as five pi over four. Now, if you're ever unsure of what the value of a rating is in degrees, you can always change the rating into degrees by multiplying by the quantity 180 over pi this will allow us to reduce both the pies to just one leaving us with five multiplied by 180 which will give us the value of 900/ multiplied by one, which will give us four and 900 divided by four will give us a final value of 225 degrees. So what this means is that our theta has the value of 225 degrees. And that means that starting at the radius of negative four, we're going to travel 225 degrees in the positive direction and that is going to put us at position ss. So what this means is that the position of the given polar coordinate, negative four comma five pi over four is going to be at position S and with that being said, the answer to this problem is going to be D. 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.

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, 5π/4)

Key Concepts

Polar Coordinates

Angle Measurement in Radians

Negative Radius in Polar Coordinates

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