The reference angle of [tex]\[{}^{\text{pi}}/{}_{\text{12}}\][/tex] is [tex]\frac{\pi }{12}[/tex].
What is reference angle?
The reference angle for a rotation is the acute angle formed by the terminal side and the [tex]$x-$[/tex] axis.
We have to find the reference angle of [tex]\[{}^{\text{pi}}/{}_{\text{12}}\][/tex].
In the image of unit circle below:
As we see in the image, the [tex]\frac{\pi }{2}[/tex] is in the first quadrant.
So, the reference angle is [tex]\frac{\pi }{12}[/tex].
If we convert the given reference angle in degree, then we get,[tex]$D=\left( \frac{R}{\pi } \right)\cdot 180$[/tex]
as
[tex]${{\pi }^{c}}=180{}^\circ $[/tex]
Where [tex]D[/tex] is the degree and [tex]R[/tex] is the reference angle.
[tex]$D=\frac{\left( \frac{\pi }{12} \right)\cdot 180}{\pi }$[/tex]
Cancel the common factor [tex]\pi[/tex].
[tex]$D=\frac{180}{12}$[/tex]
[tex]$\therefore D=15{}^\circ $[/tex]
Hence, the reference angle is [tex]\frac{\pi }{12}[/tex] and in degree is [tex]15{}^\circ $[/tex].
Learn more about reference angle here
https://brainly.com/question/10613177?
#SPJ2
