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!!