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.

420°

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 the angle we are working with is 390 degrees and we are provided a blank unit circle. The first thing I notice about 390 degrees is that it is greater than a full rotation of our unit circle which is 360 degrees. So this means in order to find out where the angle 390 degrees lies, I need to first subtract 360 degrees from it at which point I will get 30 degrees is the angle I'm looking for. So in standard position, one side of our angle is on the positive side of the X axis. And we wanna find where 30 degrees is. Well, I know the positive side of the X axis is zero degrees and degrees. And I know the positive side of the y axis is 90 degrees. So I know that 30 is between zero and 90. So so far, we know we are working in quadrant one now to find to 30 degrees in the first quadrant, you can reference another unit circle or this is broken into thirds right now. So 30 degrees would be at this first line within the unit circles. First quadrant and my line is not perfect, but it should fall on to the line. So our angle falls in quadrant one and has a reference angle of 30 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.
420°