The reference angle of \(\[{}^{\text{pi}}/{}_{\text{12}}\]\) is \(\frac{\pi }{12}\).
What is reference angle?
The reference angle for a rotation is the acute angle formed by the terminal side and the \($x-$\) axis.
We have to find the reference angle of \(\[{}^{\text{pi}}/{}_{\text{12}}\]\).
In the image of unit circle below:
As we see in the image, the \(\frac{\pi }{2}\) is in the first quadrant.
So, the reference angle is \(\frac{\pi }{12}\).
If we convert the given reference angle in degree, then we get,\($D=\left( \frac{R}{\pi } \right)\cdot 180$\)
as
\(${{\pi }^{c}}=180{}^\circ $\)
Where \(D\) is the degree and \(R\) is the reference angle.
\($D=\frac{\left( \frac{\pi }{12} \right)\cdot 180}{\pi }$\)
Cancel the common factor \(\pi\).
\($D=\frac{180}{12}$\)
\($\therefore D=15{}^\circ $\)
Hence, the reference angle is \(\frac{\pi }{12}\) and in degree is \(15{}^\circ $\).
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