Question

How do you find the exact value of $\sin \dfrac{7\pi }{6}$?

Answer 1

In this problem, we have to find the exact value of the given trigonometric sine function. We can see that the given degree value is above ${{360}^{\circ }}$, so we can split them into part, where we can inverse the function based on the first degree value inside the bracket and we can find the degree value of the resulted function.

Complete step by step answer:
We know that the given function to find its value is,
$\Rightarrow \sin \dfrac{7\pi }{6}$
We can see that the given degree value is above ${{360}^{\circ }}$, so we can apply the reference angle method to find the exact value.
We can now find the reference angle by finding equivalent trig values in the first quadrant.
We know that the reference angle for the given angle is,
$\Rightarrow \sin \dfrac{\pi }{6}$
We can now make the expression negative because sine is negative in the third quadrant, we get
$\Rightarrow -\sin \dfrac{\pi }{6}$
We know that the degree value for the above step is a negative half,
$\Rightarrow -\dfrac{1}{2}$
We can now write I in the exact form, we get
$\Rightarrow -0.5$

Therefore, the exact value of $\sin \dfrac{7\pi }{6}$ is -0.5

Note: Students make mistakes while finding the reference angle where the given degree value is above ${{360}^{\circ }}$. We should also remember that we can find the reference angle by finding equivalent trig values in the first quadrant. We should make the expression negative because sine is negative in the third quadrant.