Question

sin(19pi/6)=

Answer 1

The sine of an angle corresponds to the triangle's y-value formed at angle on the unit circle.

2pi is one full rotation around the unit circle.

We can write 19pi/6 as 12pi/6 + 7pi/6.

The 12pi/6 is actually 2pi, and be neglected, so we consider the residual angle, 7pi/6.

sin(19pi/6) = sin(7pi/6).

7pi/6 is like half a rotation and then pi/6 more.

So we're in the third quadrant now, with an angle of pi/6 below the x-axis.

We know that sin(pi/6) = 1/2. So sin(7pi/6) = -1/2.

Therefore sin(19pi/6) = -1/2.