00:01
Find all the solutions of this trigonometric equation.
00:04
And i'll look at it.
00:05
It is quadratic in form.
00:06
So i'm going to rewrite this as 2x squared minus 2x minus 1.
00:11
Just to make it a little cleaner here.
00:13
And i see i have to use the quadratic formula to solve this.
00:17
So my quadratic formula says we're going to take negative b, my b being negative 2 plus or minus the square root of negative 2 squared minus 4a, c over 3.
00:30
To 8, which will be 2, and that's going to be 4.
00:34
So we're going to have 4 plus 8, so that's going to be 12.
00:40
Now, we could go ahead and break this down into the simple radical, but there's really no need.
00:46
Well, let's go to do it, because it will make our life a little bit easier.
00:49
Let's go 2 plus or minus 2 squares of 3 over 4, which will be 1 plus or minus the square of 3 over 2.
00:57
But you could leave it in this form.
00:59
It really doesn't matter.
01:00
So we have x then.
01:03
It's going to be 1 plus the square to 3 over 2.
01:06
And x is going to be 1 minus the square to 3 over 2.
01:10
So that's going to end up being a positive value.
01:13
That's going to end up being a negative value.
01:15
That's important because we know that cosine of theta is going to equal as 1 plus the square to 3 over 2.
01:23
Cosine of theta is going to equal 1 minus the square to 3 over 2.
01:29
So i'm going to look, i like to draw pictures of these...