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Chapter 1: Problem 68

\( 1 \mathrm{rad}=\ldots \ldots \ldots \ldots\) (a) \(180^{\circ}\) (b) \(3.14^{\circ}\) (c) \((180 / \pi)^{\circ}\) (d) \((\pi / 180)^{\circ}\)

Short Answer

Expert verified
\(1 \mathrm{rad} = (180 / \pi)^{\circ}\)

Step by step solution

01

Recall the relationship between radians and degrees

One circle is 360 degrees or \(2\pi\) radians. Therefore, the relationship between degrees (D) and radians (R) can be given by: D = R * (180 / π) We are given that R = 1 rad.
02

Calculate the degrees corresponding to 1 radian

From the above equation, we can calculate the degrees corresponding to 1 radian: D = 1 * (180 / π)
03

Identify the correct option

Now let's compare our result with the given options: (a) \(180^{\circ}\): Incorrect, because 1 radian is less than \(2\pi\) radians and cannot be equal to 180 degrees. (b) \(3.14^{\circ}\): Incorrect, because this option is close to π, not the degrees corresponding to 1 radian. (c) \((180 / \pi)^{\circ}\): Correct, because this equation matches our calculated result of D = 1 * (180 / π). (d) \((\pi / 180)^{\circ}\): Incorrect, because this option gives the conversion factor from degrees to radians, not the degrees corresponding to 1 radian. So, the correct answer is \((c) (180 / \pi)^{\circ}\).

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