Question:

Convert the point from rectangular coordinates to spherical coordinates.

a. b. c. d.

e.

Relevant equations :

tanθ = y/x

ρ = √(x²+y²+z²)

Φ = arccos(z/ρ)

Solution attempt:ρ=√(7²+(7√3)²+14²) = 14√2

tanθ = 7√3/-7 = -√3 arctan(-√3) = -Π/3

Φ = arccos(14/14√2) = Π/4

Now my issue is that as you can see -Π/3 is not an option in the multiple choice for θ. I assume the answer is then Π/3 but I’m a little unsure why I didn’t get that as my answer.