Question

Find the value by referring to the graph of the sine function.
sin(3/2pi)

Answer 1

Do you know the unit circle?

Answer 2

not very well

Answer 3

Ok it's a circle with radius = 1.

You also need to know:
pi/2 radians = 90 degrees
pi radians = 180 degrees
3pi/2 radians = 270 degrees
2pi radians = 360 degrees


0 radians is when the radius is pointing perfectly to the right and you measure the angle counter-clockwise.

Answer 4

If you're thinking about sine, you think about the y value for a certain angle rotation whereas if you think about cosine, you think about the x value for a certain angle rotation.

In the case of your problem,
The angle, let's call it theta, theta = 3*pi/2 and we have sine, so we want to determine what's the y value that the end of the radius reaches when the radius is at an angle of 3*pi/2 (radians) = 270 degrees, which is -1.

So, now you know that, sin(3*pi/2) = -1. So, on the graph of sin(x), find the coordinate (theta,sin(theta) = (3*pi/2, -1).

Answer 5

Sorry if my explanation sucks, I have a major headache from working too hard. :(

Answer 6

so -1 would be my final answer?

Answer 7

-1 is the final answer, NUMERICALLY, but the problem wanted you to be able to find the point (3*pi/2,-1) ON THE GRAPH OF sin(x) (so I guess you need to graph sin(x) yourself or just find the point (3*pi/2,-1) on a graph already drawn for you) and not by using the unit circle. The unit circle is just a way to simplify things ... it might not seem simple if this is the first time you're seeing it, but it does help you think faster when you know the concepts well.

It's not wrong to use the unit circle if it helps you find the correct point (3*pi/2,-1) on the graph of sin(x), but you need to involve the graph of sin(x) in your work.