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).

2

Accepted Answer

Welcome back. Everyone in this problem, we want to determine the equivalent degree measure of seven radiance. And we want to express our answer to the nearest minute for our answer choices. A is 401 degrees and four minutes B is 802 degrees and eight minutes C is 601 degrees and six minutes and D is 200 degrees and 32 minutes. Now, what are we trying to figure out here? Well, as it said, we want the equivalent degree of measure for our seven radiance. So the question is, what do we know about degrees and radiance? Well, recall, OK, that P radiance is actually equal to 180 degrees. So for our figure that we want that is seven radiance, we're trying to figure out how much degrees seven radiance is equal to. So to do that, we can cross multiply. Now, when we do that, then we'll find that means the number that we need our value. OK, will be equal to 180 degrees multiplied by seven radians. OK, let me write that a little better here multiplied by several radis divided by high radiance. Now, that we have that we can go ahead and convert to degrees. So let's do that 180 multiplied by seven equals 1260. So our answer is going to be 1260 divided by pi degrees. Ok. No, let's go for a calculator to help us 1260 divided by pi when we do that, we'll get 401.07 degrees. Therefore several adis is equivalent to 401.07 degrees. But now remember if we look back in our problem, we want to express our answer to the nearest minute. So if we have 0.07 degrees, we need to convert that to minutes. We know that 60 minutes equals one degree, right? So since 60 minutes equals one degree, then 0.07 degrees multiplied by 60 will give us how many minutes is in 0.07 degrees. Now recall that seven times six is 42. So 0.07 times 60 would be equal to 4.2. So that's 4.2 minutes. We wanted our answer to the nearest minute. So when we round that we'll get approximately four minutes. Therefore, seven A is actually equal to or equivalent to 401 degrees and four 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).

2

Key Concepts

Radian to Degree Conversion

Understanding Minutes in Angle Measurement

Rounding and Precision in Angle Conversion

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