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Chapter 0: Problem 4

Convert each angle to radian measure. $$ 405^{\circ} $$

Short Answer

Expert verified
The angle \(405^{\circ}\) in radians is \(\frac{9\pi}{4}\).

Step by step solution

01

Identify the given angle

The given angle is \(405^{\circ}\).
02

Apply the conversion factor

To convert the angle from degrees to radians, multiply it by the conversion factor \(\frac{\pi}{180}\) radians: \[ radians = 405^{\circ} \times \frac{\pi}{180}\]
03

Simplify

Now, we simplify the equation by multiplying 405 with \(\frac{\pi}{180}\): \[ radians = \frac{405\pi}{180}\] We see that both numbers in the fraction (405 and 180) are divisible by 45. \[ radians = \frac{9\pi}{4}\] The angle in radians is \(\frac{9\pi}{4}\).

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