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.

7𝜋 6

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 given is five pi divided by four. We are also given a blank unit circle. The first thing I consider is whether five pi divided by four is more or less than one full rotation of our unit circle. Knowing that a full rotation is too high. I can say that in terms of a common denominator that would be eight pi divided by four since five pi divided by four is smaller. I know that it is only one ro rotation. It is within 0 to 2 pi. So I don't have to worry about subtracting or adding anything next in standard form or standard position. I know that one side of my angle is on the positive side of the X axis from there. I need to decide where does the other side of this angle lie. So I'm gonna label my axes with their radiant measures. So the positive side of the X axis is zero or two pie Y, the positive side of Y is pi divided by two. The negative side of the X axis is pi, the negative side of the Y axis is three pi divided by two. So comparing our values, I'm gonna make a common denominator, you know, I'm gonna start with pie. So if I want to draw pie in terms of fourths, this would be four pi divided by four. Since five pi divided by four is greater than that. We know it is not in quadrant one or two. It will likely being quadrant three. But I wanna verify that and I'm gonna do that by rewriting three pi divided by two, a six pi divided by four, five pi divided by four, definitely falls between four pi divided by four and six pi divided by four. So it will be in quadrant three. Now looking for the exact measure I can reference another unit circle if I need to, but this is exactly the middle of quadrant three. So five pi divided by four on our unit circle would have a sketch like this where it is in the middle of quadrant three 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.
7𝜋 6