# Math Help - converting rectangular to spherical coordinates

1. ## converting rectangular to spherical coordinates

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.

2. ## Re: converting rectangular to spherical coordinates

Hey shmiks.

Hint: 7√3/7 = 1/√3. You wrote x as 7 in calculating rho: is it 7 or -7?