00:01
Okay, this equation i want to solve in the range 0 to 2 pi.
00:05
So the first step, get the same trick function all the way through if you can.
00:12
Here, i don't want 4x and 2x.
00:15
Let's get 2x all the way through.
00:17
Sign 4x, i can write as 2, sine 2x, cos 2x.
00:25
Now that comes from the double angle formula, which is the sine of 2a.
00:34
Is twice sine a cos a so if a is 2x then we get sign 4x equals what i have here and that equals 0 now i can factor out sine 2x so i get sign of 2x 2x 2 cos 2x minus 1 equals 0 which means either sign 2x equals 0 or 2 cos 2x minus 1 equals 0 and both of these i can solve pretty quickly.
01:24
This one, well in the sign graph i know that zero occurs as 0 pi 2 pi 3 pi 4 pi and so on and so on.
01:39
So x itself then must be 0, pi by 2, pi and 3 pi by 2.
01:50
4 pi is too large for the range requested.
01:55
Doesn't include 2 pi.
01:58
So there we have four answers.
02:03
Now look at the other one over here.
02:08
That becomes cos 2x equals 1 1⁄2.
02:12
And from that, well, one half is plus...