(a) Sketch the curve represented by the polar equation: r = 2 + sinθ (b) Find...

(a) Sketch the curve represented by the polar equation: r = 2 + sinθ

(b) Find the points on the given polar curve where the tangent line is horizontal or vertical, and what is the tangent line at θ = π/3?

Expert Solution

milcah answered 2 years ago

sketch the curve with the given polar equation by first sketching the graph of r as...

sketch the curve with the given polar equation by first sketching the graph of r as a function of theta in Cartesian coordinates. 1) r = 3cos(3theta) 2) r = 1 + 3cos(theta) 3) r = sin (theta / 2) Please solve this problem with a detailed explanation, not just a answer.

Sketch the curve with the given polar equation by first sketching the graph of r as...

Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates. r = 3 cos(2θ)

Sketch a graph of the polar equation and find the length and area of the curve in one loop.

What is the area inside the polar curve r = 1 , but outside the polar curve r = 2 cos θ ?

What is the area inside the polar curve r=1, but outside the polar curve r=2cosθ?

1. Find a Cartesian equation for the curve. r cos(θ) = 2 Identify the curve. 2....

1. Find a Cartesian equation for the curve. r cos(θ) = 2 Identify the curve. 2. Find a Cartesian equation for the curve. r = 4 sin(θ) Identify the curve.

r(t)=sinti+costj. - Sketch the plane curve represented by r and include arrows indicating its orientation. -...

r(t)=sinti+costj. - Sketch the plane curve represented by r and include arrows indicating its orientation. - Sketch the position vector r(t), the velocity vector r′(t), and the acceleration vector r′′(t) for the two times t = π/2, 5π/4 , putting the initial points of the velocity and acceleration vectors at the terminal points of the position vectors. - Prove that the vectors r(t) and r′(t) are orthogonal for every t.

Find the area of the region enclosed by the polar curve r = 3−cos(6θ).

1. (a) Sketch the slope field for the given differential equation: dy/dx = 2? (b) Find...

1. (a) Sketch the slope field for the given differential equation: dy/dx = 2? (b) Find the particular solution of the differential equation that satisfies the initial condition y(0) = 4 (c) What is the value of y when x = 1/2 2. (a) Find the general solution of the given differential equation: dy/dx = ysinx = ????? 2 (b) Find the particular solution of the differential equation that satisfies the initial condition ? = 2; ?ℎ?? ? = π/2

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The spiral of Archimedes is a curve described in polar coordinates by the equation ?? =...

The spiral of Archimedes is a curve described in polar coordinates by the equation ?? = ???? where ?? is the distance of a point from the origin, and ?? is the angle of the point in radians with respect to the positive x-axis. Write an m-file to create a plot of the spiral of Archimedes using 1000 points for 0 ? ?? ? 6?? ?????? when k = 0.5. Be sure to include a title, axis labels, and grid...

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