In Exercises 35–60, find the reference angle for each angle.17𝜋6

Question

Accepted Answer

Hello, today we're going to be calculating the reference angle for eight pi over three. So the first thing we wanna do is we want to figure out where eight pi over three is located on the unit circle. If you're ever unsure about where a radiant is located at, you can always convert the radiant to a degree. In order to do this, we can multiply eight pi over three by 1 80 over pi doing this allows us to reduce both of the pies to one. And what we are left with is eight times 180 which is going to give us 1440. And in the denominator, we have three times one, which is three, 1440 divided by three is going to give us 480 degrees. So one thing to note is that this region, this angle lies outside of the region of one rotation of the unit circle. The unit circle has a total of 360 degrees. So what we're going to need to do is we're going to need to rewrite this angle in standard form. So that it is an angle that lies between zero degrees and degrees. In order to do this, we're going to take 480 degrees and subtract 360 degrees from this amount. Doing so allows us to rewrite this angle as 120 degrees. Now, we need to ask ourselves where is 120 degrees located on the unit circle while 120 degrees is located in the second quadrant of the unit circle. Now that we know the location of the angle, we need to go ahead and calculate the reference angle. The reference angle is always located between our given angle and the x axis of the unit circle. And since this angle exists in quadrant two, in order to get this reference angle, we're gonna take 180 degrees and subtract our given angle which is 120 degrees, 180 degrees minus 120 degrees is going to give us 60 degrees. Now, this is gonna be the measurement of the reference angle and we're going to convert 60 degrees back into radiant. In order to do this, we're going to take 60 degrees and multiply it by pi over 80 doing this gives us the value of 60 pi over 180. And this fraction is going to simplify to leave us with pi over three. So what this means is that the reference angle for eight pi over three is going to be pi over three. And with that being said, the answer to this problem is going to be C 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 35–60, find the reference angle for each angle.17𝜋6

Key Concepts

Reference Angle

Angle Measurement

Quadrants of the Unit Circle

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