Convert each degree measure to radians. Leave answers as multiple...

Question

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).  ​​                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                 
 ―1800°

Accepted Answer

Hey, everyone in this problem, we're asked to determine the equivalent radiant measure of negative 2160 degrees. We're given four answer choices. Option A negative 38 pi divided by three, option B negative 40 pi divided by three, option C negative 12 pi and option D negative nine pi. So let's start by recalling the relationship between degree and radiant measure and we want to convert one to the other. We have to think about the relationship between the two and we know that 180 degrees is equivalent to pie. So if we take our degree value and we divide it by 180 degrees, that's gonna be equal to our radiant value X that we're looking for divided by pi. OK. So on the left, we're looking at the ratio of our value to 180 degrees. That's gonna be the same as the ratio of our radiance to pi because we know 180 degrees is equivalent to pi ratings and we know the degree value so we can write negative 2160 degrees divided by 180 degrees will be equal to X divided by pi you can multiply both sides by pi. We get that X is going to be equal to, we have degrees divided by degrees. So the units are actually going to divide out. So we're just gonna have negative 2160 divided by 180 pi and we can simplify this fraction when we do that, we're gonna get that X is equal to negative 12. And that is that answer we were looking for, that is negative 2160 degrees in radiance. And that's gonna correspond with answer choice C. That's it for this one. Thanks everyone for watching. See you in the next video.

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―1800°

Key Concepts

Degree to Radian Conversion

Understanding π (Pi)

Multiples of π

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