In Exercises 41–56, use the circle shown in the rectangular coord...

Question

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

-210°

Accepted Answer

Hello, everyone. We are given an angle and asked to identify the quadrant where it lies and sketch it in standard position on the unit circle. Provided we are given the angle negative 240 degrees and we are provided a blank unit circle. So the first thing I notice is that this is negative, which means in standard position, one side of our angle will be on the positive side of the X axis. And we need to find out where the other side is because it's negative, we would start at the positive side of the X axis and go down and clockwise around our unit circle. I'm not good with counting backwards with negatives. I'd rather make a positive reference angle and I can do that by adding a full rotation or 360 degrees to my negative angle. So negative 240 degrees plus 360 degrees is gonna give me positive 120 degrees. This is my reference angle. So I at least can think a little bit easier because positive numbers come easier for me when I label my axes, I know the positive side of the X axis. Is zero degrees or 360 degrees. I know that the Y axis, the positive side there is 90 degrees. I know the negative side of the X axis is 180 degrees and the negative side of the Y axis is 270 degrees. This will help me locate where 120 degrees would fall. So I can find where negative 240 degrees would fall. 120 degrees would be between 90 and 1 80. So that would be in quadrant two. So that means that the angle negative 240 degrees is in quadrant two. And whether you access a unit circle that has all the measures on it, or if you recall from graphing previously, 120 degrees would be the first line to the left of the y axis in quadrant two. So this means that when we start at the positive side of the X axis and go clockwise, we'd land in quadrant two for the angle negative 240 degrees have a nice day.

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In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
-210°