For the first one, if is positive then the angle can be in either the first or third quadrant. You have to look at the context (a diagram ?) to decide which.
For the second one,
I have 2 problems that i am stuck on
1) Find a set of cylindrical coordinates (with r ≥ 0 and 0 ≤ θ < 2π) of the point whose Cartesian coordinates are given. (-5, -5, -4)
i have already found r and z, which are (5sqrt(2), ? ,-4) and have confirmed that those 2 are correct but i cannot find the right answer for theta.
This is what i have tried but it is not the correct answer and i do not know why.
theta = arctan(-5/-5)
theta = arctan(1) = pi/4 (wrong?!?!?! why?!?!)
2) Find a set of spherical coordinates (with ρ ≥ 0, 0 ≤ ϕ ≤ π and 0 ≤ θ < 2π) of the point whose Cartesian coordinates are given.(0, – 5√3, 5)
On this one, i already solved for rho and p but not for theta.
(10, arctan((sqrt(75))/5) , ? )
This is what i have tried but i dont understand how you can divide by zero.
tan(theta) = y/x
theta = arctan(5sqrt(3)/0) (divide by zero?!?! what?!?!)
Can anyone help? THANKS!!