00:01
So in this problem, you're being asked to solve the given trig equation.
00:03
So the first thing we need to do is we need to isolate our trig function.
00:07
So to do this, we're going to start by dividing both sides of our equation by two.
00:11
So when we divide both sides of our equation by two, that will leave us with the sine squared of 2x equal to 1 half.
00:20
So again, we have the sine squared of 2x equals 1 half.
00:31
And i apologize, my computer's being a little slow.
00:34
Okay, so now we have to get rid of the sine squared part.
00:37
In other words, we have to get rid of the square root of both sides.
00:42
So to do that, we're going to take the square root of both sides, equal to, remember, when you take the square root of both sides is plus or minus, and then we have the square of the one, which is one, but we can't simplify the square root of two.
00:53
But we can rationalize this by multiplying the numerator and the denominator by root two.
00:58
So that leaves us with the sign of 2x equal to plus or minus root 2 over 2.
01:03
All right, so now typically we would be sitting here thinking, well, what values for our angle give us a sign value of root 2 over 2? now, before we do that, we have this 2 here in the middle.
01:16
Now, that too means that this graph is going to cycle through two times from 0 to 2 pi...