We shall break the given angle into rotation and an angle
[tex]\frac{7\pi }{6}= \frac{6\pi+\pi }{6}= \frac{6\pi }{6}+ \frac{\pi }{6}=\pi+\frac{\pi }{6}[/tex] [tex]
So the reference angle for [tex]\frac{7\pi }{6}[/tex] is [tex]\frac{\pi }{6}[/tex]
Also [tex]\pi+\frac{\pi }{6}[/tex] lies in quadrant 3.
In quadrant 3 sin is negative
So
[tex]sin(\frac{7\pi }{6})= sin(\pi+\frac{\pi }{6} ) = - sin\frac{\pi }{6}= - \frac{1}{2}[/tex]
Hence the reference angle of 7π/6 is π/6 and sin (7π/6) = -1/2.
