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Chapter 5: Problem 4

Convert these to radian measure: (a) \(30.0^{\circ},\) (b) \(135^{\circ}\) (c) \(\frac{1}{4}\) revolution, (d) 33.3 revolutions.

Short Answer

Expert verified
Question: Convert the following angle measures: (a) 30.0 degrees, (b) 135 degrees, (c) 1/4 revolution, (d) 33.3 revolutions. Answer: (a) \(\frac{\pi}{6}\) radians, (b) \(\frac{3\pi}{4}\) radians, (c) \(\frac{\pi}{2}\) radians, (d) \(66.6\pi\) radians.

Step by step solution

01

(a) Convert 30.0 degrees to radians.

To convert an angle from degrees to radians, we can use the following formula: Radians = Degrees × \(\frac{\pi}{180}\) Now, let's convert 30.0 degrees to radians using this formula: Radians = 30.0 × \(\frac{\pi}{180}\) = \(\frac{\pi}{6}\) Therefore, \(30.0^{\circ}\) is equal to \(\frac{\pi}{6}\) radians.
02

(b) Convert 135 degrees to radians.

Next, let's convert 135 degrees to radians using the same formula: Radians = 135 × \(\frac{\pi}{180}\) = \(\frac{3\pi}{4}\) Therefore, \(135^{\circ}\) is equal to \(\frac{3\pi}{4}\) radians.
03

(c) Convert 1/4 revolution to radians.

To convert a fraction of a revolution to radians, we can use the following formula: Radians = Fraction × \(2\pi\) Now, let's convert \(\frac{1}{4}\) revolution to radians using this formula: Radians = \(\frac{1}{4}\) × \(2\pi\) = \(\frac{\pi}{2}\) Therefore, \(\frac{1}{4}\) revolution is equal to \(\frac{\pi}{2}\) radians.
04

(d) Convert 33.3 revolutions to radians.

Finally, let's convert 33.3 revolutions to radians using the same formula: Radians = 33.3 × \(2\pi\) = \(66.6\pi\) Therefore, 33.3 revolutions are equal to \(66.6\pi\) radians.

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