To determine the reference angle for [tex]\(\theta = \frac{11\pi}{6}\)[/tex], we need to understand in which quadrant this angle lies and then find the appropriate reference angle formula for that quadrant.
The angle [tex]\(\frac{11\pi}{6}\)[/tex] is greater than [tex]\(\pi\)[/tex] but less than [tex]\(2\pi\)[/tex]:
1. Determine the quadrant:
- An angle between [tex]\(\pi\)[/tex] and [tex]\(2\pi\)[/tex] lies in the fourth quadrant.
2. Referring to the fourth quadrant:
- In the fourth quadrant, the reference angle [tex]\(\alpha\)[/tex] is calculated using [tex]\(\alpha = 2\pi - \theta\)[/tex].
Given [tex]\(\theta = \frac{11\pi}{6}\)[/tex], the reference angle calculation is:
[tex]\[
\alpha = 2\pi - \theta = 2\pi - \frac{11\pi}{6}
\][/tex]
Thus, the correct statement showing how to calculate the reference angle for [tex]\(\theta = \frac{11\pi}{6}\)[/tex] is:
[tex]\[
2\pi - \theta
\][/tex]
The numerical result, calculated accurately, would be approximately [tex]\(0.5235987755982991\)[/tex] radians.
