00:01
Okay, so we're finding out when is sine of x, sign of 2x, sorry, equals a negative square to 3 over 2.
00:13
And that is from 0 to 2 pi.
00:17
That can be written as inequalities, that interval notation there.
00:24
And you're ultimately looking for x, not 2x.
00:29
So in order to solve this equation, my equation has 2x in it.
00:34
So we're going to take this inequality and we're going to multiply everything by 2.
00:43
That means that when we're looking in unit circle, we're going to go around a unit circle twice.
00:48
Once is 2 pi, twice would give me 4 pi.
00:51
So we're going to look at our circle for a sign value of negative square to 3 over 2 and find those angles.
00:57
In other words, we're looking for a y value that's negative square to 3 over 2.
01:01
So here's a unit circle right here.
01:05
So sign y value negative square to 3 over 2 occurs at 4.
01:08
Pi over three and five pi over three.
01:14
So again that was four pi over three and five pi over three.
01:22
But that is just going around the unit circle once.
01:25
So if i'm here, for example, at four pi over three, i've got around the unit circle one time and i want to get back to four pi over three because i'm going around second time, going all the way back around.
01:35
I have to get back to the star.
01:38
That means i'm going around one more time or a full circle, which is two pi...