Using equivalent angles, the equivalent expression is:
[tex]-\sin{\frac{\pi}{12}}[/tex]
--------------------
- Angles between 0 and 90º(0 and 0.5π) are in the first quadrant.
- Angles between 90º and 180º(0.5π and π) are in the second quadrant.
- Angles between 180º and 270º(π and 1.5π) are in the third quadrant.
- Angles between 270º and 360º(1.5π and 2π) are in the fourth quadrant.
- Each angle will have equivalents in other quadrants.
--------------------
- The expression given is: [tex]\sin{\frac{13\pi}{12}}[/tex].
- The angle [tex]\frac{13\pi}{12}[/tex] is in the third quadrant.
- To find the equivalent angle in the first quadrant, for an angle in the third quadrant, 180º = π is subtracted from the angle.
Then:
[tex]\frac{13\pi}{12} - \pi = \frac{13\pi}{12} - \frac{12\pi}{12} = \frac{\pi}{12}[/tex]
The equivalent expression is, considering that in the third quadrant and in the first quadrant, the sine has opposite signals.
[tex]-\sin{\frac{\pi}{12}}[/tex]
A similar problem is given at https://brainly.com/question/23843479
