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).

-47.69°

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the equivalent reading measure of negative 58 degrees 38 minutes and to express the answer to the nearest 1000th, our answer choices are answer choice. A negative 1.023. Answer choice B negative 4.023. Answer choice C negative 0.512 and answer choice D negative 2.047. All right, we are converting from degrees to radiance. However, what we're given isn't entirely in degrees yet, we still have this 38 minutes, but we can convert from minutes to degrees. We recall from previous lessons that one degree equals 60 minutes. So we can take our 38 minutes and multiply that by in the numerator, one degree divided by 60 minutes in the denominator. And now our minutes units cancel out and we can multiply straight across 38 multiplied by one is 38 divided by 60. That's degrees. But we can simplify this 38 divided by 60 simplifies to be 19, divided by 30 that's degrees. So what we have here is this is all negative. So I'll put negative and then parentheses, we have 58 degrees plus another 19/30 of a degree. And if you add what's in the parentheses, you can put 58 plus 19 divided by 30 in your calculator, you'll get 1759 divided by 30. Now remember that this is negative in its degrees. So there's our negative 58 degrees, 38 minutes expressed entirely in degrees. Now to convert from degrees to radiance, we recall from previous lessons that we are going to multiply by in the numerator pi radiance and that's divided by in the denominator 180 degrees. Now our degrees units cancel out and we can multiply straight across negative 1759 multiplied by pi is negative 1759 pi divided by in the denominator 30 multiplied by 180 is 5400. This is radiance, but we're asked to express our answer to the nearest 1000th. So you can plug into your calculator negative 1759 pi divided by 5400 you'll get approximately negative 1.0233 that keeps going but rounding to the 1000th. So we, that's the third decimal place. We look at this three looks to the next three and it remains a three. So we have a negative 1.023 that is in radiance. There is our negative 58 degrees 38 minutes expressed in Radians. We look at our answer choices for negative 1.023 and that matches with answer choice. A 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).
-47.69°

Key Concepts

Degree to Radian Conversion

Negative Angles

Rounding Numbers

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