How do you convert spherical coordinates to rectangular coordinates?
How do you convert spherical coordinates to rectangular coordinates?
Convert from spherical coordinates to rectangular coordinates
- x=ρsinφcosθ
- y=ρsinφsinθ
- z=ρcosφ
How does PHI work in spherical coordinates?
Phi is the angle between the z-axis and the line connecting the origin and the point. The point (5,0,0) in Cartesian coordinates has spherical coordinates of (5,0,1.57). The surfaces pho=constant, theta=constant, and phi=constant are a sphere, a vertical plane, and a cone (or horizontal plane), respectively.
What is the equation in Cartesian rectangular coordinates equivalent to this equation in spherical coordinates consider the equation ρ 2cosφ?
Rectangular coordinates ( x , y , z ) ( x , y , z ) and spherical coordinates ( ρ , θ , φ ) ( ρ , θ , φ ) of a point are related as follows: x = ρ sin φ cos θ These equations are used to convert from y = ρ sin φ sin θ spherical coordinates to rectangular z = ρ cos φ coordinates.
How are spherical polar coordinates related to the rectangular Cartesian coordinates?
The spherical coordinates are related to the rectangular Cartesian co-ordinates in such a way that the spherical axis forms a right angle similar in a way that the line in the rectangle whose coordinates are generated through the perpendicular axis.
How do you describe a sphere in spherical coordinates?
In the spherical coordinate system, a point P in space is represented by the ordered triple (ρ,θ,φ), where ρ is the distance between P and the origin (ρ≠0),θ is the same angle used to describe the location in cylindrical coordinates, and φ is the angle formed by the positive z-axis and line segment ¯OP, where O is the …
Can Phi be negative in spherical coordinates?
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.
How do you convert polar equations to rectangular equations?
To convert from polar coordinates to rectangular coordinates, use the formulas x=rcosθ and y=rsinθ.
How do you solve spherical coordinates?
The equation ϕ=π/2 corresponds to the xy-plane. or √x2+y2=ρsinϕ. (Given that 0≤ϕ≤π, we know that sinϕ≥0 and the positive square root is ρsinϕ.) If we divide by z=ρcosϕ, we obtain a formula for ϕ in terms of Cartesian coordinates √x2+y2z=tanϕ.