FINAL CALC EXAM

Question 1

Polar to Rectangular equations

Answer 1

(r, θ) -> (x, y)
x = rcos(θ)
y = rsin(θ)

Question 1

Rectangular to Polar equations

Answer 1

(x, y) -> (r, θ)

r^2 = x^2 + y^2
tan(θ) = y/x

Question 2

Rectangular to Cylindrical equations

Answer 2

(x, y, z) -> (r, θ, z)
r^2 = x^2 + y^2
tan(θ) = y/x
z = z

Question 3

Cylindrical to Rectangular equations

Answer 3

(r, θ, z) -> (x, y, z)
x = rcos(θ)
y = rsin(θ)
z = z

Question 4

Rectangular to Spherical equations

Answer 4

(x, y, z) -> (ρ, θ, φ)
ρ^2 = x^2 + y^2 + z^2
tan(θ) = y/x
cos(φ) = z/sqrt(x^2 + y^2 + z^2)

Question 5

Spherical to Rectangular equations

Answer 5

(ρ, θ, φ) -> (x, y, z)
x = ρsin(φ)cos(θ)
y = ρsin(φ)sin(θ)
z = ρcos(φ)