Question

What is the sine value of 7 pi over 6? negative square root 3 over 2 square root 3 over 2 negative 1 over 2 1 over 2?

Answer 1

First thing to do is to change the radians to degrees so it's easier to determine our angle and where it lies in the coordinate plane.  $\frac{7 \pi }{6} * \frac{180}{ \pi }=210$.  If we sweep out a 210 degree angle, we end up in the third quadrant, with a 30 degree angle.  In this quadrant, x and y are both negative, but the hypotenuse, no matter where it is, will never ever be negative.  So the side across from the 30 degree reference angle is -1, and the hypotenuse is 2, so the sine of this angle, opposite over hypotenuse, is -1/2

Answer 2

Answer:

-1/2.

Step-by-step explanation:

Let's decompose $\frac{7\pi}{6}$:

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

So,

$sin(\frac{7\pi}{6})=sin(\pi+\frac{\pi}{6})$

$=sin(\pi)cos(\frac{\pi}{6})+sin(\frac{\pi}{6})cos(\pi)$

$=\frac{1}{2}(-1)=\frac{-1}{2}.$