In Exercises 13–17, find a positive angle less than 360° or 2𝜋 t...

Question

In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle.
31𝜋
6

Accepted Answer

Hello, everyone. We are asked to find an angle that is co terminal with the angle pi divided by four. This angle should be between zero and two pi our answer choices are a seven pi divided by four B three pi divided by eight C three pi divided by four D eight pi divided by seven. First recall that conterminal angles start in standard position. And what differs with them is how many times it goes all the way around the circle prior to ending at the terminal side. So one full rotation of a circle is two pi radium. So the angle we are given is 27 pi divided by four. And if we want this to be a co terminal angle between zero and two pi, we need to subtract two pi from it to get rid of one rotation. So that way we can subtract as many rotations as possible until we are at the base rotation that is between zero and two pi. So subtracting 27 pi divided by four by two pi, we need to have a common denominator. So we will be doing 27 pi divided by four minus eight pi divided by four which will leave us with 19 pie divided by four. Since 19 pi divided by four is still greater than two pie. I'm gonna subtract another complete rotation. So I'm subtracting two pi again. So we will be doing 19 pi divided by four minus eight pi divided by four which gives us 11 pie divided by four looking at 11 pi divided by four. This is still greater than two pie. So we are gonna subtract another two pie for another rotation. So we'll have 11 pi divided by four minus eight pi divided by four. And this will leave us with three pi divided by four which is between zero and two pi. So this is our co terminal angle and it's answer choice C have a nice day.

In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle. 31𝜋 6

Key Concepts

Coterminal Angles

Radians and Degrees

Finding Positive Angles

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