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).

122° 37'

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the equivalent radiant measure of 144 degrees 46 minutes. We're asked to express the answer to the nearest 1000th. Our answer choices are answer choice. A 5.527. Answer choice B 5.053. Answer choice C 2.527 and answer choice. D 1.684. All right. We need to convert from degrees to radiance and we're going to use unit conversion, but we don't have our given completely in degrees yet. We have this 46 minutes, but we can convert from minutes to degrees. We recall from previous lessons that one degree is equal to 60 minutes. So if we take our 46 minutes and multiply that by one degree divided by 60 minutes, now our minutes units cancel out. We can multiply straight across 46. Multiplied by one is 46 divided by 60. That's degrees. And we can simplify 46 divided by 60. That's going to be 23 divided by 30 degrees. And so what we're saying is that we have 144 degrees plus another 23/30 of a degree. And when we add those, we get, you can plug that into your calculator. You get 4343 divided by 30 degrees. And now taking our 4343 divided by 30 degrees and converting that degrees to radiance, we recall from previous lessons, we're going to multiply our degrees by pi radians in the numerator divided by 180 degrees in the denominator. Now, our degrees units cancel out, we can multiply straight across in the numerator. We have 4343 pi divided by in the denominator 30 multiplied by 180 is 5400. And that's radiance and because they want the answer to the nearest 1000th, you can plug that into a calculator. 4343 pi divided by 5400. And you get something like 2.5266 that keeps going rounding to the 1000th place. That's the third decimal spot. The six looks to the this six and it rounds up. So we will have 2.5 to 7 radians and that is our 144 degrees 46 minutes expressed in radiance. We look at our answer choices and this matches with answer choice. See, 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).

122° 37'

Key Concepts

Degree to Radian Conversion

Understanding Minutes in Angles

Rounding Numbers

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