3. Geodesics in R2 : Consider 2D flat space in polar coordinates r and θ. Find...

3. Geodesics in R² : Consider 2D flat space in polar coordinates r and θ. Find the curves parametrized by r(s) and θ(s) that satisfy the geodesic equation, and show that they correspond to straight lines in R²

Expert Solution

The metric for the plane in polar coordinate is given by,

genius_generous answered 1 year ago

The Cartesian coordinates of a point are given. (a) (−3, 3) (i) Find polar coordinates (r, θ)...

The Cartesian coordinates of a point are given. (a) (−3, 3) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) = b. (5,5sqrt(3)) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find...

Two vectors in polar coordinates (R, θ) are given byV1 = (5.0, 125°) and V2 =...

Two vectors in polar coordinates (R, θ) are given byV1 = (5.0, 125°) and V2 = (4.0, 260°). Find the sum V1 + V2 in polar coordinates. Give the answer to 2 significant figures for the magnitude and to the nearest degree in angle. Hint: first convert the vectors to Cartesian form and add them to get the resultant vector. Then convert this resultant vector to polar form

The Cartesian coordinates of a point are given. (a) (2, −5) (i) Find polar coordinates (r,...

The Cartesian coordinates of a point are given. (a) (2, −5) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) = (b) (-2, −2) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) =...

Find the polar coordinates of a point with the Cartesian coordinates

Find the polar coordinates of a point with the Cartesian coordinates (x,y)=(−4√2,4√2).

In Matlab: Any complex number z=a+bi can be given by its polar coordinates r and θ,...

In Matlab: Any complex number z=a+bi can be given by its polar coordinates r and θ, where r=|z|=sqrt(a^2+b^2) is the magnitude and θ= arctan(ba) is the angle. Write a function that will return both the magnitude r and the angle θ of a given complex numberz=a+bi. You should not use the built-in functions abs and angle. You may use the built-in functions real and imag.

Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 1 + 2 cos θ, θ = π/3

Question

3. Geodesics in R2 : Consider 2D flat space in polar coordinates r and θ. Find...

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Expert Solution

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The Cartesian coordinates of a point are given. (a) (−3, 3) (i) Find polar coordinates (r, θ)...

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For the following exercises, find the polar coordinates of the point.

For the following exercises, find the polar coordinates of the point.

For the following exercises, find the polar coordinates of the point.