What is the reference angle of π/6?
Understand the Problem
The question is asking for the reference angle of π/6, which is the smallest acute angle between the terminal side of the given angle and the x-axis.
Answer
The reference angle of $\frac{\pi}{6}$ is $\frac{\pi}{6}$.
Answer for screen readers
The reference angle of $\frac{\pi}{6}$ is $\frac{\pi}{6}$.
Steps to Solve
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Identify the angle The given angle is $\frac{\pi}{6}$ radians.
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Determine the quadrant Since $\frac{\pi}{6}$ is between 0 and $\frac{\pi}{2}$, it lies in the first quadrant.
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Calculate the reference angle For angles in the first quadrant, the reference angle is the angle itself. Thus, the reference angle is:
$$ \text{Reference angle} = \frac{\pi}{6} $$
The reference angle of $\frac{\pi}{6}$ is $\frac{\pi}{6}$.
More Information
The reference angle is simply the angle itself when it is in the first quadrant, which is the case for $\frac{\pi}{6}$.
Tips
- Confusing the quadrant: Ensure to check which quadrant the angle lies in; this determines how to find the reference angle.
- Miscomputing the angle: Remember that reference angles are only in the range of 0 to $\frac{\pi}{2}$.
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