00:01
This problem says, why is the sine of an angle more than 2 pi in radian measure always between negative 1 and positive 1? and when we think of our angle measurements as far as from 0 to 2 pi to start or 0 pi to 2 pi, when we're evaluating to find sine of the angle, whatever it may be, we're really looking for the y value on the unit circle.
00:20
So the most extreme or the greatest values we can see for sine are at pi over 2 and 3 pi over 2, where the sine of pi over 2 would be equal to positive 1 and then the sine of this 3 pi over 2 would be equal to negative 1 and everything else would be less than those values and closer to 0.
00:39
And when we start to see angles get greater than 2 pi, that means that we've made one full revolution for our angle around the unit circle.
00:49
But just because our angle is greater than 2 pi after we make that full revolution, doesn't mean that the y values at our evaluations of the angles are going to be any bigger.
00:57
So for instance, when we are in the 0 to 2 pi range, this first angle measurement is pi over 6.
01:04
That tells us that the y value at that point from the point square root 3 over 2, 1 half, would tell us that the y value is 1 half...