Convert each radian measure to degrees. Write answers to the n...

Question

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

-5.01095

Accepted Answer

Welcome back. Everyone. In this problem, we want to determine the equivalent degree measure of negative 9.03048 radiance. And we want to express our answer to the nearest minute for our answer choices. A is negative 1034 degrees. 49 minutes. B is negative 517 degrees, 25 minutes, C is negative 776 degrees seven minutes and D is negative 258 degrees and 42 minutes. No, we are trying to find the equivalent degree measure of a value expressed in radiance. So we have to ask ourselves, what do we know about degrees and radiance? Well, recall, OK, that Pyres is equivalent to 180 degrees. So this is something that we know this is a given. No, we have our value negative. Let me put that in right here for what we don't know. We have our value negative 9.03048 radiance, but we don't know how much degrees it's equal to. So how can we figure that out? Well, we could go ahead and cross multiply because by doing that, we'll find that our unknown value will be equal to negative 9.03048. Oops, let me write that properly here. Mhm 03048 radiance um multiplied by 180 degrees and that's going to be divided by pi radiance. So now if we put this into our calculator, we should be able to figure out how many degrees negative 9.03048 radiance is. Now when we work this expression out, we'll find that it equals negative 517.41 degrees. OK. So that's our equivalent value in degrees. But the problem is we are expressing our answer to the nearest minute. However, this isn't written in minutes or degree has a decimal part. So we need to convert the decimal part to minutes. So how can we do that? Well, Ricardo, because we also know all right, that one degree equals 60 minutes. So since one degree is 60 minutes, then we can take our decimal part, 0.4. Let me put that in red again, 0.41 degrees and we can convert it to minutes. We can do that by multiplying 0.41 by 60. OK. So that'll be 0.41 multiplied by 60 minutes. Now, when we do that, if we put that into our calculator, we'll find that it's approximately equal to 25 minutes. So now that we have the degrees and minutes, we can combine them because that means therefore that negative 9.03048 radiance will be equivalent to negative 517 degrees and 25 25 minutes. Ok. When we look back on our answer choices, that would have been answer choice. B thanks a lot for watching everyone. I hope this video helps.

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

-5.01095

Key Concepts

Radian to Degree Conversion

Understanding Minutes in Angles

Negative Angles

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