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pshichka [43]
3 years ago
8

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)
Mathematics
1 answer:
PolarNik [594]3 years ago
3 0

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

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Alternatively, you can calculate it this way.

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