Find the reference angle in radians for a rotation of 5pi/6.
Check the final answer first, then review the worked steps.
Check the final answer first, then review the worked steps.
1. Understand Reference Angles: A reference angle is the acute angle formed between the terminal side of an angle and the x-axis. It is always positive.
2. Locate the Angle: The given angle is $\frac{5\pi}{6}$. This angle is in the second quadrant because it is between $\frac{\pi}{2}$ (90 degrees) and $\pi$ (180 degrees).
3. Calculate the Reference Angle: In the second quadrant, the reference angle is found by subtracting the given angle from $\pi$.
Reference Angle = $\pi - \frac{5\pi}{6}$
4. Perform Subtraction: To subtract, find a common denominator, which is 6.
Reference Angle = $\frac{6\pi}{6} - \frac{5\pi}{6}$
Reference Angle = $\frac{6\pi - 5\pi}{6}$
Reference Angle = $\frac{\pi}{6}$