12.6#4

Theta can be found with the following formula, right?

arctan(y/x).   

The coordinate for this problem is (-3, 4, -1), and none of the follow are accepted:

arctan(4/-3) = -0.927295218001612 = -53.1301023542

The previous problem didn't have this issue, and the first entry for this problem accepts the following:

-3/(cos(arctan(4/-3))

Is there a way to fix this, or do I need to do something differently?

*************************************************************It requires a slightly more sophisticated notion of arctan.
The graph of the tangent function, with it's vertical asymptotes looks like this: This function doesn't satisfy the horizontal line test, so it has no inverse function. The red part of the graph is restriction of the domain of tan(x) to (-π/2, π/2), and it does satisfy the horizontal line test and the inverse function of this is what we USUALLY call arctan. These values of theta correspond to (x,y) in the first and fourth quadrants, where x>0.  The point (-3,4) is in the second quadrant though, and if you look at the angle of this point from the positive x-axis its going to have θ>π/2, corresponding to the blue curve on the right, or π-0.927295218001612 = 2.214