In Exercises 2–4, convert each angle in degrees to radians. Expre...

Question

In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.

315°

Accepted Answer

Hey, everyone in this problem we're asked to write the angle given below in radiance, ok? And we're told to write our answer in terms of pi and the angle we're given is 230 degrees, ok? And we're given four answer choices. All of them in radiant. Option A is 230 pi divided by 18. Option B is 230 pi option C is 18 pi divided by 23 and option D is 23 pi divided by 18. So we're gonna get started and we're given degrees, ok? And we wanna know what this is equal to in radiant. So we're gonna write 230 degrees is equal to X where X is gonna be in radiant. Now, what we're gonna do is we're gonna create ratios, ok? So the ratio of our degrees to 180 degrees is gonna be equal to the ratio of our radiance divided by pires, ok? Now this is because we know that 180 degrees is equal to pi radiance. So we're dividing by the same thing on either side. So the ratio of our degrees to 180 is the same as our ratio of radiance to pi because 180 degrees is equal to pi radiance, ok? Now that we have our ratio set up, we can go ahead and cross multiply, ok? So we're gonna have that X multiplied by 180 degrees is equal to 230 degrees multiplied by pi radiance. This tells us that X is equal to 230 degrees divided by 180 degrees multiplied by pi radiance. And we're asked to leave our answer in terms of pi So we're gonna leave pi alone. We're gonna simplify this fraction, 230 degrees divided by 100 and 80 degrees. The unit of degrees is going to divide it. OK? Both numerator and denominator are divisible by 10. So let's go ahead and divide the entire fraction by 10. See that this is equal to 23 divided by 18, multiplied by pi radiance. OK? And so that is our equivalent angle written in radiance, we have 230 degrees is equal to 23 divided by 18 pi radiant which corresponds with answer choice. D thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 315°

Key Concepts

Degrees and Radians

Conversion Formula

Multiples of π

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