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.15°

Accepted Answer

Hey, everyone in this problem, we're asked to write the angle given below in radiance and to express our answer in terms of pi. So we're given the angle of 25 degrees and we have four answer choices all in radiant. Option A five pi option B five pi divided by six, option C pi divided by 36 option D five pi divided by 36. Yeah, what we have is 25 degrees and we wanna know what this is equal to in radiance and we're gonna call that X. OK. So 25 degrees is equal to some number of radiant. Now, what do we know about the relationship between degrees and radiance? Can you recall that 180 degrees is equal to pi radiance? So we're gonna create ratios in our equation here. On the left hand side, we're gonna divide by 180 degrees. And so we're looking at the ratio of our angle to 180 degrees. And on the right hand side, we're gonna divide by pi radiant. OK? So we're looking for the ratio between our radiant value to pi radiance and we can do this because 180 degrees is equal to pi radiance. So it's like we're dividing by the same thing on both sides. Now, we're asked to leave this in terms of pi so what we're gonna do is we're gonna multiply both sides by pi radiance. We get that X is equal to 25 degrees divided by 180 degrees multiplied by pi radiance. OK? So now we have the value of X R radiance and all we need to do is simplify. OK? So we have 25 degrees divided by 180 degrees. The unit of degrees is gonna cancel and we just need to simplify the fraction. OK? Now, both of these numbers are divisible by five. So let's go ahead and divide the numerator and denominator by five. And that's gonna give us five divided by 36 we're still multiplying by pi radiance. And so our angle of 25 degrees is gonna be equivalent to five pi divided by 36 radiant which corresponds with answer choice D. That's it for this one. Thanks everyone for watching. I hope this video helped.

In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.15°

Key Concepts

Degrees and Radians

Conversion Formula

Multiples of π

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