Question

Which expression is equivalent to sin?

Answer 1

Using equivalent angles, the equivalent expression to $\sin{\left(\frac{7\pi}{6}\right)}$ is:

$\sin{\left(\frac{11\pi}{6}\right)}$

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 $\frac{7\pi}{6}$ is on the third quadrant, as $\pi < \frac{7\pi}{6} < \frac{3\pi}{2}$. Hence the equivalent angle on the first quadrant is:

$\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}$

The sine is negative on the third and fourth quadrants, hence the equivalent angle on the fourth quadrant is:

$2\pi - \frac{\pi}{6} = \frac{11\pi}{6}$

Thus, the equivalent expression is:

$\sin{\left(\frac{11\pi}{6}\right)}$

More can be learned about equivalent angles at brainly.com/question/24787111

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Answer 2

Answer: Option 4

Step-by-step explanation:

$\sin \frac{7\pi}{6}=\sin \left(-\frac{\pi}{6} \right)=\sin \frac{11\pi}{6}$