Using equivalent angles, it is found that the equivalent expression to [tex]\sin{\frac{7\pi}{6}}[/tex] is given by:
[tex]\sin{\frac{11\pi}{6}}[/tex]
What is the equivalent angle to the one in this problem?
The angle is of [tex]\frac{7\pi}{6}[/tex], which is in the third quadrant, as [tex]\pi \leq \frac{7\pi}{6} \leq \frac{3\pi}{2}[/tex].
The equivalent in the first quadrant is given by:
[tex]\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}[/tex]
However, the sine is positive in the first and second quadrant, and negative in the third and fourth, hence the equivalent angle on the fourth quadrant is given by:
[tex]2\pi - \frac{\pi}{6} = \frac{12\pi}{6} - \frac{\pi}{6} = \frac{11\pi}{6}[/tex]
Hence the equivalent expression is:
[tex]\sin{\frac{11\pi}{6}}[/tex]
More can be learned about equivalent angles at https://brainly.com/question/24787111
