00:02
So if we model this equation as a quadratic, in other words, if we say we have x squared plus 2x minus 1 is equal to 0, minus 1 is equal to 0, and remember that we're setting x equal to tangent of omega.
00:21
Well, if we use the quadratic formula here, negative 2 plus or minus the square root of 4 minus 4 times negative 1 times 1, all over 2.
00:34
Gives us this gives value of negative 1 plus or minus plus or minus this gives us this gives root 8 so root 8 can be and be rewritten as as root 4 times root 2 and so root 4 it comes 2 so we have 2 root 2 divided by 2 this gives us plus or minus root 2 and so now we have that that tangent of omega is equal to negative 1 plus square root of 2 and tangent of omega is equal to negative 1, negative 1, and then we have minus root 2.
01:13
Well, we know that the square root of 2 is larger than 1.
01:20
So if we have negative 1 plus a root 2, this is going to be positive.
01:25
And then, so let's write this here.
01:26
So this will be positive.
01:27
And a negative 1 minus negative root 2 is going to be negative.
01:30
So when we're solving for our first value here, we're going to have that omega, omega is going to be equal to the tangent or tangent inverse...