Spherical Coordinates (need work double checked please)

In summary, the conversation is about a problem where the person has done multiple attempts and received the same answer, but the online submission says it is wrong. They ask for someone to double check their calculations and provide their attempt at a solution. Another person suggests using a trigonometric identity, but the first person is unsure if it can be used for two different angles.
  • #1
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Could someone double check to make sure my calculations are all done right? I've done this problem several times and gotten the same answer but the online submission says its wrong so I need someone else to check my work. thanks!


Homework Statement




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Homework Equations



x = ρ sin(Φ) cos(θ)
y = ρ sin(Φ) sin(θ)
z = p cos(Φ)

The Attempt at a Solution



4z2 = x2+y2

4p 2cos2(Φ) = ρ 2sin2(Φ) cos2(θ) + ρ 2sin2(Φ) sin2(θ)

cos2(Φ) = (ρ 2sin2(Φ) cos2(θ) + ρ 2sin2(Φ) sin2(θ))/ (ρ 2 *4)

***(ρ2's cancel right?)****

so I'm left with for an answer

cos2(Φ) = (sin2(Φ) cos2(θ) + sin2(Φ) sin2(θ))/ 4)
 
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  • #2
How about using the fact that [itex]sin^2(\theta)+ cos^2(\theta)= 1[/itex]?!
 
  • #3
I didn't think you could use that when your are talking about two different angles (Φ and θ)?

I tried it anyway though and its a no go...
 
  • #4
What HallsOfIvy meant was that you should factor out sin2(Φ) in the numerator of your final expression and apply that trigo identity. That will simplify your final answer.
 

FAQ: Spherical Coordinates (need work double checked please)

1. What are spherical coordinates?

Spherical coordinates are a system of coordinates used to locate points in three-dimensional space. They consist of a radial distance from a fixed point, an azimuth angle measured from a reference direction, and an elevation angle measured from a reference plane.

2. How do you convert Cartesian coordinates to spherical coordinates?

To convert Cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ), use the following equations:
r = √(x² + y² + z²)
θ = arctan(y/x)
φ = arccos(z/r)

3. What is the significance of spherical coordinates in physics?

Spherical coordinates are commonly used in physics to describe the position and motion of objects in three-dimensional space. They are particularly useful in situations involving spherical symmetry, such as gravitational or electromagnetic fields.

4. Are there any limitations to using spherical coordinates?

One limitation of spherical coordinates is that they cannot be used to describe points at the origin (r = 0). Additionally, they can be difficult to use in situations where the reference direction or reference plane is not well-defined.

5. How are spherical coordinates used in real-world applications?

Spherical coordinates have a wide range of applications, including in navigation, astronomy, and geology. They are also commonly used in computer graphics and 3D modeling to represent the position of objects in virtual environments.

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