Question

If we start at the point (1,0) and travel once around the unit circle, we travel a distance of 2 pi units and arrive back where we started at the point (1,0). If we continue around the unit circle a second time, we will repeat all the values of x and y that occurred during our first trip around. Use the this discussion to evaluate the following expressions

sin (2pi + 3pi/2)

Answer 1

Answer:

-1

Step-by-step explanation:

We evaluate $\sin(2\pi+3\pi/2)$

In $2\pi+3\pi/2$, $2\pi$ is a complete revolution and is the same as 0. So we have

$\sin3\pi/2 = \sin(\pi+\pi/2)$

One $\pi$ is a half revolution, putting the point at (-1, 0). $\pi/2$ is a quarter of a revolution. A quarter circle from (-1, 0) anticlockwise is (0, -1).

The sine is the y-coordinate of a point along a unit circle.

Hence, $\sin(2\pi+3\pi/2)=-1$