Find the reference angle for the angle \( -\frac{33 \pi}{4} \) The reference angle is Type your answer in radians. Txpe an integer or a simplified fraction.)
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Bonus Knowledge
To find the reference angle for \( -\frac{33 \pi}{4} \), we first convert it to a positive angle by adding \( 2\pi \) (or \( \frac{8\pi}{4} \)) until we get a positive angle. Adding \( 2\pi \) multiple times gives us: \[ -\frac{33 \pi}{4} + 8\pi = -\frac{33 \pi}{4} + \frac{32 \pi}{4} = -\frac{\pi}{4} \] Now, to convert \( -\frac{\pi}{4} \) to a positive angle: \[ -\frac{\pi}{4} + 2\pi = -\frac{\pi}{4} + \frac{8\pi}{4} = \frac{7\pi}{4} \] The angle \( \frac{7\pi}{4} \) lies in the fourth quadrant. The reference angle is calculated as: \[ 2\pi - \frac{7\pi}{4} = \frac{8\pi}{4} - \frac{7\pi}{4} = \frac{\pi}{4} \] Thus, the reference angle for \( -\frac{33 \pi}{4} \) is: \[ \frac{\pi}{4} \]
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