00:01
We want to find teter in this equation where teter is between 0 and 2 pi radiant, not inclusive of 2 pi radian.
00:09
Note that this is the quadratic equation in cosine teter.
00:14
Let's factorize it.
00:17
We will have cosine teter minus 4 and 2 cosine theta plus 1.
00:25
So cosine theta minus 4 is equal to 0 or 2 cosine titter plus 1 is equal to 0.
00:33
So cosine teter is equal to 4 or 2 cosine teter equals to minus 1 or cosine titter will be minus half.
00:48
For cosine teter equals to 4, i will have to reject since cosine teter is always being bounded by negative 1 and 1 for all teter.
01:01
For cosine titter equals to minus half, you will need to know the frigo window.
01:07
Here is zero radian, going anti -clockwise, you have pi over two radian here.
01:13
Over here you have pi radiance.
01:15
Over here is 3 pi over two radiance, and coming back up, you have two pi -radian.
01:21
Now, you can go anti -clobwise as many cycles as you like.
01:26
In the next cycle, you can just add 2 pi to every angle you see, and in the next next cycle, you'll just add 4 pi to every angle you see and so on and so forth.
01:34
Between 0 and pi over 2 radian, this is what we call the first quadrant going anti -clockwise.
01:41
This is the second quadrant, third quadrant and fourth quadrant.
01:46
In the first quadrant, all three goals are positive.
01:50
In the second quadrant, only sign is positive.
01:53
In the third quadrant, only tangent is positive.
01:56
And in the fourth quadrant, only cosine is positive...