Using equivalent angles, the equivalent expression to [tex]\sin{\left(\frac{7\pi}{6}\right)}[/tex] is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
What are equivalent angles?
Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, we have that [tex]\frac{7\pi}{6}[/tex] is on the third quadrant, as [tex]\pi < \frac{7\pi}{6} < \frac{3\pi}{2}[/tex]. Hence the equivalent angle on the first quadrant is:
[tex]\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}[/tex]
The sine is negative on the third and fourth quadrants, hence the equivalent angle on the fourth quadrant is:
[tex]2\pi - \frac{\pi}{6} = \frac{11\pi}{6}[/tex]
Thus, the equivalent expression is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
More can be learned about equivalent angles at https://brainly.com/question/24787111
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