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Chapter 0: Problem 1

Convert each angle to radian measure. $$ 150^{\circ} $$

Short Answer

Expert verified
The angle in radians is \(\frac{5\pi}{6}\).

Step by step solution

01

Identify the angle in degrees

The angle given in the problem is \(150^\circ\).
02

Apply the conversion factor

To convert the angle to radians, multiply the angle in degrees by the conversion factor \(\frac{\pi}{180}\): \[150^\circ \times \frac{\pi}{180}\]
03

Simplify the expression

Now, we will simplify the expression: \[150 \times \frac{\pi}{180} = \frac{150\pi}{180}\] To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which in this case is 30: \[\frac{150\pi}{180} = \frac{150\div30}{180\div30}\] \[\frac{150\pi}{180} = \frac{5\pi}{6}\] So, the angle in radians is: \[\boxed{\frac{5\pi}{6}}\]

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