Question

The measure of angle θ 7pi/6 is . The measure of its reference angle is °, and sin θ is

Answer 1

Answer:

30° and -1/2. This is pretty easy to do on a piece of paper but I recommend googling "unit circle" and clicking images, it tells you everything you need to know.

Answer 2

We shall break the given angle into rotation and an angle

$\frac{7\pi }{6}= \frac{6\pi+\pi }{6}= \frac{6\pi }{6}+ \frac{\pi }{6}=\pi+\frac{\pi }{6}$ $So the reference angle for [tex]\frac{7\pi }{6}$ is $\frac{\pi }{6}$

Also $\pi+\frac{\pi }{6}$ lies in quadrant 3.

In quadrant 3 sin is negative

So

$sin(\frac{7\pi }{6})= sin(\pi+\frac{\pi }{6} ) = - sin\frac{\pi }{6}= - \frac{1}{2}$

Hence the reference angle of 7π/6 is π/6 and sin (7π/6) = -1/2.