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For the given angle [tex]\theta[/tex], identify the reference angle [tex]\varphi[/tex].

[tex]\theta = \frac{11 \pi}{6}[/tex]

A. [tex]\varphi = \frac{\pi}{6}[/tex]
B. [tex]\varphi = \frac{\pi}{3}[/tex]
C. [tex]\varphi = 2 \pi[/tex]

Sagot :

GinnyAnsweridn
To solve for the reference angle, we need to understand the concept of reference angles and how they relate to the given angle [tex]\(\theta\)[/tex].

First, let's identify the quadrants of the given angle. The given angle is [tex]\(\theta = \frac{11\pi}{6}\)[/tex]. Since [tex]\(\frac{11\pi}{6}\)[/tex] is in the fourth quadrant, we need to find the reference angle.

The reference angle, [tex]\(\varphi\)[/tex], for any angle [tex]\(\theta\)[/tex] located in the fourth quadrant is calculated using the formula:
[tex]\[ \varphi = 2\pi - \theta \][/tex]

Substituting [tex]\(\theta = \frac{11\pi}{6}\)[/tex] into the formula:
[tex]\[ \varphi = 2\pi - \frac{11\pi}{6} \][/tex]
[tex]\[ \varphi = \frac{12\pi}{6} - \frac{11\pi}{6} \][/tex]
[tex]\[ \varphi = \frac{12\pi - 11\pi}{6} \][/tex]
[tex]\[ \varphi = \frac{\pi}{6} \][/tex]

So the reference angle [tex]\( \varphi = \frac{\pi}{6} \)[/tex].

Thus, the correct answer is [tex]\(\frac{\pi}{6}\)[/tex].
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