Drawing curves in Spherical coordinate

In summary, 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), and φ = arccos(z/r). The difference between polar coordinates and Spherical coordinates is that polar coordinates are two-dimensional and use an angle and distance from the origin, while Spherical coordinates are three-dimensional and use two angles and a distance from the origin. To plot a curve in Spherical coordinates, determine the equations for r, θ, and φ in terms of a parameter, and then plug in different values to generate a set of points. The length of a curve in S
  • #1
athrun200
277
0
I had a tutorial today and my tutor said these questions are very trivial so we can simply look at it at home.

But after going home, I found that I don't know how to do Q 35.
I know that p<3 is responsible for the big sphere with r=3. But I don't know why the other part is responsible for the small sphere

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  • #2
hi athrun200! :smile:

hint: draw a circle with B at the bottom, centre O, and any point P

then BP = 2OBcosOBP :wink:
 

1. 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)

2. What is the difference between polar coordinates and Spherical coordinates?

Polar coordinates are a two-dimensional system that uses an angle and distance from the origin to describe a point, while Spherical coordinates are a three-dimensional system that uses two angles and a distance from the origin to describe a point.

3. How do you plot a curve in Spherical coordinates?

To plot a curve in Spherical coordinates, you first need to determine the equations for r, θ, and φ in terms of a parameter, such as t. Then, you can plug in different values for t to generate a set of points, which can be plotted in a three-dimensional graph.

4. How can you calculate the length of a curve in Spherical coordinates?

To calculate the length of a curve in Spherical coordinates, you can use the arc length formula:

L = ∫√(r² + (dr/dt)² + (r sin φ (dθ/dt))² + (r (dφ/dt))²) dt

5. What are some real-life applications of drawing curves in Spherical coordinates?

Spherical coordinates are commonly used in physics, engineering, and astronomy to describe the position and movement of objects in three-dimensional space. They are also used in computer graphics to create 3D models and animations, as well as in navigation systems to track the position of objects in the sky.

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