if 0 smaller and equal θ smaller and equal 2 pi, find sin(7pi/6)

Question

if 0 smaller and equal θ smaller and equal 2 pi, find sin(7pi/6)

show works please

Answer 1

Mary, this is how to tackle this: (layout is very important)

sin(7π/6) = sin(π/6 + π) . . . . which shows that our angle, 7π/6, is in Q3 => sin is -ve

= -sin(π/6)

= -1/2

Answer 2

7pi/6 is counterclockwise rotation of pi(6pi/6) + pi/6

so you are in quadrant 3 with reference angle pi/6

sin is negative in quadrant 3 so this is -1/2