Why is theta used in spherical coordinates?

The coordinates used in spherical coordinates are rho, theta, and phi. Rho is the distance from the origin to the point. Theta is the same as the angle used in polar coordinates. Phi is the angle between the z-axis and the line connecting the origin and the point.

What does Phi range from in spherical coordinates?

Definition of spherical coordinates ρ = distance to origin, ρ ≥ 0 φ = angle to z-axis, 0 ≤ φ ≤ π θ = usual θ = angle of projection to xy-plane with x-axis, 0 ≤ θ ≤ 2π Easy trigonometry gives: Hold φ and θ fixed, and let ρ increase.

How do you evaluate integrals in spherical coordinates?

To evaluate a triple integral in spherical coordinates, use the iterated integral ∫θ=βθ=α∫ρ=g2(θ)ρ=g1(θ)∫u2(r,θ)φ=u1(r,θ)f(ρ,θ,φ)ρ2sinφdφdρdθ.

Why is theta from 0 to pi?

It’s because the area you are looking for is a product of the and components, not and the angle . Sweeping the values of across the circle as changes at a constant rate will cover the circle in an non-uniform way.

Why is PHI only from 0 to pi?

You only need to integrate phi from 0 to pi to sweep out the full volume of the sphere.

Is Phi Always 0 to pi?

you want to let θ to from 0 to 2π and φ go from 0 to π, otherwise the sin(φ) factor can be negative. If you don’t do that you need absolute values around the sine factor, generally causing twice the work, or worse, incorrect calculation by being unaware of that.

What is Theta in cylindrical coordinates?

Cylindrical coordinates are a simple extension of the two-dimensional polar coordinates to three dimensions. The polar coordinate θ is the angle between the x-axis and the line segment from the origin to the point.

Why is phi from 0 to pi?

Does order of integration matter for spherical coordinates?

In general integrals in spherical coordinates will have limits that depend on the 1 or 2 of the variables. In these cases the order of integration does matter.