Convert each degree measure to radians. If applicable, round t...

Question

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

56° 25'

Accepted Answer

Welcome back. I am so glad you're here. We are asked to determine the equivalent radiant measure of 48 degrees. 35 minutes express the answer to the nearest 1000th. Our answer choices are answer choice. A 2.848 answer choice. B 0.848 answer choice C 0.565 and answer choice. D 1.696. All right. We are given degrees and we are converting it into radiance. We're going to use unit conversion for that. But before we start converting to radiance, we need to make sure our whole number is in degrees and we have this 35 minutes, which is not in degrees yet, but we can use unit conversion for that too. We recall from previous lessons, that one degree is equal to 60 minutes. So if we take our 35 minutes and multiply that by the unit, we'll put one degree in the numerator divided by 60 minutes in the denominator. Now, our minute units cancel out, we can multiply straight across 35 multiplied by one is 35 divided by 60 that's degrees. We can simplify 35 divided by 60 simplifies to 7/12 and there's our degree. So what we have is 48 degrees plus 7/12 of a degree. Now, we want to combine those, so you can plug that into a calculator and that will be 583 divided by 12 degrees. So that's what we're dealing with 583 divided by 12 degrees. And we want to convert that into radiance. So to convert degrees to radiance, we multiply by pi radiance in the numerator divided by 180 degrees in the denominator. Now, our degrees units cancel out, we can multiply straight across in the numerator. That's 583 pi divided by, in the denominator, 12 times 12, multiplied by 180 is 2160. And that's radiance and we're asked to give our answer expressed to the nearest 1000th. So you can plug that into a calculator. 583 pi divided by 2160. And you'll get something like 0.8479 and that will continue. But the 1000th is the third decimal place. That's the seven looks to the nine and it's going to round up. So this will be 0.848. And our unit is radiance. That is the equivalent radiant measure of 48 degrees 35 minutes. We look at our answer choices and 0.848 radiance matches with answer choice b well done. We'll catch you on the next one.

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

56° 25'

Key Concepts

Degree to Radian Conversion

Converting Minutes to Decimal Degrees

Rounding to the Nearest Thousandth

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