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).

3.06

Accepted Answer

Welcome back. Everyone in this problem, we want to determine the equivalent degree measure of 6.48 radiance to the nearest minute for our answer choices. A is 371 degrees and 17 minutes. B is 185 degrees and 38 minutes. C is 556 degrees and 55 minutes. And D is 774 degrees and 33 minutes. Now, if we are going to find the equivalent degree measure of 6.48 radiance, we need to understand the relationship between radiance and degrees. So, what do we know? Well, recall that Pyridium is equal to 180 degrees. That's what we already know. We have 6.48 radians. Ok. Let me write that properly here. 6.48 radiance. And we'd like to know how many degrees it's equal to. So how can we figure that out? Well, notice there, we can do a bit of cross multiplying. Ok. And when we do that, we'll find that 6.48 radians in degrees represented here will be equal to 6.48 radians, 6.48 radiance. Multiplied by 180 degrees divided by pi radiance. So if we work the salt, we should be able to find how much 6.4 radiance is in degrees. So let's go ahead and do that. Now, if we use our calculator, we'll find that 6.48 multiplied by 180 equals 1166.4. So we're going to divide that by pi to find out how much it is in degrees. No, 1166.4 divided by pi equals 371.28. So 6.48 radiance is equal to 371.28 degrees. Now, we're almost there. Remember we're writing our answer to the nearest minute here. Our degree has a decimal part. So we need to convert that to minutes. So what else do we know? Well, again, recall that one degree equals 60 minutes. So if we want to convert 0.28 degrees to minutes, ok, then to do that, we're going to multiply 0.28 by 60 minutes. Now, when we do that, you'll find that 0.28 degrees in minutes equals 16.8 minutes. But we're not done yet because we have to write it to the nearest minute. So to the nearest minute, that would be 17 minutes. Therefore, there are four, since we have both parts, 6.48 radiance equals 371 degrees and 17 minutes. When we look back on our answer choices, that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

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

3.06

Key Concepts

Radian to Degree Conversion

Degrees and Minutes

Precision in Trigonometric Calculations

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