00:01
All right, we're told that the secant of x is 6 over 5, and we know that it's in quadrant 4.
00:13
So we can also write that the cosine of x is the reciprocal of that, which is going to be 5 over 6, right? so in quadrant 4, it's 5 in the x direction, and then this is going to be 6.
00:33
Let me move that over.
00:34
So this is 5 in the x direction like that.
00:37
And then we don't know what that is, so we can solve.
00:39
So 5 squared plus i'll just put the question mark squared is equal to 6 squared.
00:46
So that's 25, and that's 36.
00:55
So this is going to be the squared of 11.
00:59
Negative.
01:01
All right.
01:02
And then from that, we could find the sine of x and the tangent of x.
01:06
The tangent of x is going to be negative 11 over square of 11 over 6 and then the tangent is opposite over adjacent or sign over cosine negative square root of 11 over 5 and then we want the half angles basically so we know that the sign of x over 2 is going to be equal to plus or minus the squared of 1 minus the cosine x over 2.
01:54
Oh, we didn't even need, that's fine.
01:57
I'll just go with it.
01:58
So plus or minus a square root of 1 minus the cosine of x is 5 over 6 over 2.
02:06
That's going to be 1 6 divided by 2.
02:09
So it's going to be plus or minus the square root of 112.
02:15
Now is it going to be positive or negative? so if this is the angle, then half the angle.
02:21
So the angle is between 270 and 360...
