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Problem 10

Degrees to Radians In Exercises 9 and 10, convert the degree measure to radian measure as a multiple of $\pi$ and as a decimal accurate to three decimal places.

$\begin{array}{lll}{\text { (a) }-20^{\circ}} & {\text { (b) }-240^{\circ}} & {\text { (c) }-270^{\circ}} & {\text { (d) } 144^{\circ}}\end{array}$

Answer

see steps for the answer

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## Discussion

## Video Transcript

this question asks us to convert each of the following four degree measures into radiant measures as multiples of pie and as decimals, accurate of three decimal places. So to begin with, A. The main thing in this problem is it. To convert from degrees to radiance, you have to multiply by a conversion factor of 360 degrees in the denominator with two pie in the numerator and so two pies equivalent of 360. And when used like this is a conversion factor, you're essentially multiplying by one just to convert it to radiance. Now, when you want to buy these two together, you get negative 40 pie over 3 60 on. That simplifies nicely to negative pint nights. That's your simplified multiple of pie version. But after plugging into calculator, you will see that this is the same as negative 0.34 That's the truth, all right, moving on to be, we need to convert negative 240 degrees and Iranians, so we use the same process in party, multiplying by that conversion factor too high. And then, after doing some algebra and some simplification with your fraction, you'll find that this is equal 24 pi over three. So that's our simplified Malta pull of a radiance version. Multiple of hi sorry, Nats equivalent to negative for 0.1 89 So by now, I'm sure you guys have the hang of it, but I'm just going to show you how to do it in part C and D is well, see, we're going to be converting the angle measure negative. 270 degrees. So negative 270 degrees multiplied by our conversion factor of 360 degrees over to pie. That's going to simplify really nicely. Right on down. Teo. Negative three. Over to pie. Someone plugged into your calculator. That's the same as they get 4.712 and then lastly, we're going to convert 144 degrees. So multiply by our conversion factor to fly over 60 degrees, and this is going to simplify right on down to 4/5 pie. When you plug that into the calculator for that decimal version to find that that's the same as 2.513 All right, there we go

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