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, −3π/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 negative three pi over four. Now, one thing to note about polar coordinates is that the general form of a polar coordinate is given to us as our comma theta. Here R represents the radius of the polar coordinate and theta represents the angle of the polar polar coordinate. So using the general form of a polar coordinate, let's first start by identifying our radius negative four is in the position of R. So our radius is equal to negative four. What this means is that we're going to be using the radius as the starting position of our polar coordinate. So if we take a look at the polar axis, notice that the polar axis has multiple circles within it, the first circle represents a circle of radius one followed by the next circle of radius two, followed by the next circle of radius three. And the final circle of radius four. Since we know that the radius of the polar coordinate is negative four, the starting position is going to be four in the negative direction of the polar axis. Next, let's identify our angle theta. Now theta is given to us as negative three pi over four. Now, if you're unsure of the exact quantity of the radiant, you can always convert the radiant into degrees by multiplying the radiant by 180 over pi doing. This allows us to eliminate the pine terms and reduce them to just one. And what we are left with is negative three, multiplied by 180 which will give us negative 540/4 multiplied by one, which will give us four and negative 540 divided by four will give us a final degree of negative 135 degrees. So in order to find the final position of the polar coordinate, we're going to have to travel 135 degrees in the negative direction of the unit circle. Now note that the positive direction of the unit circle is in the counterclockwise position. If we want to triangle travel in a negative direction, we're going to have to travel in the clockwise position. So starting at the circle of radius negative four, we're going to travel a total of 135 degrees in the negative direction. And that is going to put us at position S. So that means the position of negative four comma negative three 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, −3π/4)

Key Concepts

Polar Coordinates

Angle Measurement in Radians

Negative Radius in Polar Coordinates

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