Convert each radian measure to degrees. See Examples 2(a) and 2(b...

Question

Convert each radian measure to degrees. See Examples 2(a) and 2(b).                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     ―8π/5

Accepted Answer

Hey, everyone in this problem, we're asked to determine the equivalent degree measure of negative nine pi divided by five. We have four answer choices all in degrees. Option A negative 264. Option B negative 162 option C negative 628 and option D negative 324. Now, we have a radiant measure. We want to find the equivalent degree measure. So we need to think about the relationship between degrees and radiance and recall that pi radiance is equivalent to 180 degrees. So what we can do is write this ratio, we can write that the ratio of the radiance we have divided by pie must be equal to the degrees. We have divided by 180 degrees. The ratio must be the same because we know pi radiance is equal to 180 degrees and we want the radiance to be equivalent to the degrees. Now, in this case, we're given the radiance and we wanna find the degrees. So let's go ahead and substitute that. We're gonna have that negative nine pi divided by five divided by pi is equal to the degrees. We'll call that X, that's what we're looking for. Divided by 180 degrees. On the left hand side, any of these pies will divide out. We can multiply by both sides by 180 degrees. So we get that X is gonna be equal to negative nine fifth multiplied by 180 degrees, which gives us an X value of negative 324 degrees. OK? So that is the answer we were looking for. If we take a look at it, it also makes sense. We know that there are two pi radians in 360 degrees. If we think about completing a circle, our radiant value was just under two pi radiance. Our degree value is just under 360 degrees. OK? So they kind of match, it makes sense. Taking a look at our answer choices, we can match what we found and see that answer choice D is going to be correct. Negative nine pi divided by five radiance is equivalent to negative 324 degrees. That's it for this one. Thanks everyone for watching. See you in the next video.

Convert each radian measure to degrees. See Examples 2(a) and 2(b). ―8π/5

Key Concepts

Radian Measure

Degree Measure

Conversion Formula

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