To determine the reference angle [tex]\( r \)[/tex] for the given angle [tex]\( \theta = \frac{1}{12} \)[/tex], we need to consider how reference angles work in various quadrants.
1. Identifying the Quadrant To Which [tex]\( \theta \)[/tex] Belongs:
The angle [tex]\( \theta = \frac{1}{12} \)[/tex] is in radians. Convert [tex]\( \theta \)[/tex] into degrees if necessary for easier understanding, knowing that:
[tex]\[
1 \text{ radian} \approx 57.2958 \text{ degrees}
\][/tex]
Therefore,
[tex]\[
\theta = \frac{1}{12} \approx 0.08333 \text{ radians}
\][/tex]
This value is very small and falls within the first quadrant (where angles range from [tex]\( 0 \)[/tex] to [tex]\( \frac{\pi}{2} \)[/tex]).
2. Finding the Reference Angle:
The reference angle [tex]\( r \)[/tex] of [tex]\( \theta \)[/tex] in the first quadrant is simply [tex]\( \theta \)[/tex] itself.
Thus, the equation used to determine the reference angle [tex]\( r \)[/tex] when [tex]\( \theta = \frac{1}{12} \)[/tex] is:
[tex]\[
r = \theta
\][/tex]
So, the appropriate equation from the given options is:
[tex]\[
r = \theta
\][/tex]
This result matches the expected value of [tex]\( r \)[/tex] for the given [tex]\( \theta \)[/tex].
