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).

139° 10'

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the equivalent radiant measure of 128 degrees. 20 minutes express the answer to the nearest 1000th. Our answer choices are answer choice. A 4.480. Answer choice. B 1.120. Answer choice C 2.240 and answer choice D 3.240. All right. So we need to get from degrees to radiance. So we need to do some unit conversion. But actually before we can convert from degrees to radiance, we need to convert from minutes to degrees. So we've got this 20 minutes here. Well, we recall from previous lessons that in one degree there are 60 minutes. So we can use unit conversion with our 20 minutes and convert that to degrees. We'll multiply 20 minutes by the unit. We'll put one degree in the numerator because that's what we want it to be divided by 60 degrees. Now, our degrees will cancel out. We can multiply straight across 20 multiplied by one is 20 divided by 60 in the denominator. That's degrees. We can simplify 20 divided by 60. That's one third. So this is one third of a degree. So, what we have here is 128 degrees plus one third of a degree. Now, we can find a common denominator or you can plug that into your calculator, but you'll need to add 128 degrees plus one third degrees and you'll get 385 divided by three degrees. Now, there is our 128 degrees, 20 minutes in degrees. So now let's work on getting that to radiance. We'll take 385 divided by three degrees. And we recall from previous lessons that when we are, when we are converting from degrees to radiance, we're going to multiply our degrees by the unit pie radiance divided by 180 degrees. Now, our degrees cancel out multiplying across the numerators will have 385 pi divided by multiplying across the denominators. Three multiplied by 180 is 540 and this is radiance. Now, we are asked to express our answer to the nearest 1000th. So you can plug into your calculator 385 pi divided by 540. And you get something like 2.2398 that keeps going. But since we're rounding to the 1000th, that's the third decimal place. That's this nine, it looks to the eight and rounds up. So we'll have 2.240 and that is radiance. We look at our answer choices and this matches with answer choice. C 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).

139° 10'

Key Concepts

Degree to Radian Conversion

Converting Minutes to Decimal Degrees

Rounding to the Nearest Thousandth

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