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