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Which equation can be used to determine the reference angle, [tex]r[/tex], if [tex]\theta=\frac{1}{12}[/tex]?

[tex]\ \textless \ br/\ \textgreater \ \begin{array}{l}\ \textless \ br/\ \textgreater \ A. \quad r=\theta \\\ \textless \ br/\ \textgreater \ B. \quad r=\pi-\theta \\\ \textless \ br/\ \textgreater \ C. \quad r=\theta-\pi \\\ \textless \ br/\ \textgreater \ D. \quad r=2 \pi-\theta\ \textless \ br/\ \textgreater \ \end{array}\ \textless \ br/\ \textgreater \ [/tex]

Sagot :

GinnyAnswer
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].
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