How do I tell which quadrant [tan^-1(-√3/3)] lies in?
I know the whole CAST thing, where it starts from quad 4 and goes up, left, down to quad 3 but i don't understand this other thing.
[tan^-1(-√3/3)]
So tan θ = -√3/3, where θ is between - pi/2 and pi/2.
So tanθ is less than 0 but how does that hell me what quadrant it's in?
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CAST says that tan is positive for angles in the 1st and 3rd quadrants. The value -√3/3 is negative, so the angle must be in the 2nd or 4th quadrants. The problem also has the angle between - pi/2 and pi/2, which means it is in quadrants 1 or 4.
Which boils down to (1) the angle is in quadrant 2 or 4, and (2) the angle is in quadrants 1 or 4.
if theta is b/w pi/2 and -pi/2, then that leaves it in either quadrant one, or four.
Tan=opposite over adjacent. To make tan(theta) less than zero, one of the numbers in the ratio has to be negative. The adjacent line is most likely negative, which makes the triangle lie in quandrant 4