00:01
Alright, so on this question you're asked to graph the function y equals sine of x over the interval 0 to 2 pi.
00:12
And you've got a graph that looks something like this.
00:14
These marks here, this is 1 half, this is the square root of 2 over 2, and the square root of 3 over 2 right here.
00:26
And then this is 1.
00:28
So if you think about the values of sine of x, using your calculator, if you take sine of x, and you may have had the unit circle so you can look at your unit circle, but the sine of 0 is 0.
00:45
And so you're going to graph the point 0, 0, and sine starts right here.
00:51
And then the sine of 2 pi is also 0, so your graph is going to end right here.
00:59
And then let's go in the middle, the sine of pi, if you go to your calculator or to your unit circle, sine of pi is equal to 0 as well, so you're going to be back right here.
01:16
And then let's go to sine of pi over 2.
01:22
So if we go to the calculator and we get sine of pi over 2, that gives us a value of 1.
01:36
And then sine of 3 pi over 2, that's the middle point right here, that's going to be negative 1.
01:51
Sine of 3 pi over 2, negative 1.
02:13
Now i'm going to take a minute here and i want to look at a unit circle because you should have been familiar with this by now.
02:25
Your unit circle, the value of your sine, let's see, here we go, sine is the second coordinate, your y coordinate.
02:42
So here, the sine of pi over 6 is pi over 2 right there.
02:49
These x, y coordinates, the x is your cosine value and the y is your sine value.
02:54
So if you're looking at the sine of pi over 6, this first blue angle, then the cosine of pi over 6 would be the square root of 3 over 2.
03:01
And the sine of pi over 6 would be 1 half.
03:05
So using that is also beneficial as opposed to using the calculator.
03:13
So we just looked at the sine of pi over 6, which is 1 half.
03:16
And then the sine of pi over 3, sine of pi over 4 is what we'll, yeah, sine of pi over 3 we'll do next.
03:30
Sine of pi over 3 is, go into your calculator, is 0 .866.
03:42
That's the square root of 7, the square root of 3 over 2.
03:46
So if we calculate the value of the square root of 3 divided by 2, whoops, square root of 3 divided by 2, then you'll get a value of 0 .866.
04:00
So the sine of pi over 3 is the square root of 3 over 2.
04:05
So it's right here.
04:08
And then if you continue to do this, pi over 4 is going to be right here halfway.
04:14
So it's not really halfway between 1, 6, 2, 6.
04:17
So pi over 4 is going to be about right here.
04:22
So this is 1 half.
04:25
The sine of pi over 4 is the square root of 2 over 2, which is right here.
04:30
And then the sine of pi over 3 is the square root of 3 over 2, which is right here.
04:36
Then your sine curve is just going to go like this.
04:42
That's not very good.
04:44
It rounds out up here.
04:47
And then it's going to come back down here.
04:57
And then pi over 6 is going to be 1 half...