Consider the polar curve r = sin(3θ). Sketch this polar curve on the interval 2π/3 ≤ θ ≤ π.

Q: What is the slope of the line tangent to the polar curve r = ㅠ Ө - ? O 1 √√3 ✓ 2 T -||♡33 √√3 cos at…

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Q: Graph the sets of points whose polar coordinates satisfy the equationsand inequalities θ= π/3, -1 ≤…

A: The polar coordinate can be represented by r, θ, where r is the length of the curve and θ is the…

Q: 4. Convert to rectangular coordinates and sketch the curve x = 4 sec 0 y = 3 tan 0

A: Here we convert parametric equation in rectangular equation. And then we draw the graph.

Q: Find the point(s) of intersection between the following two polar curves on the interval [0, 360]: r…

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Q: . Let the parametric equations of the plane curve C be x = 2 cos t, y = 4 sin t, 0<t < 2n ). Find…

A: The parametric equations can be converted into cartesian equation by removing t. This can be done by…

Q: Consider the polar curves C1 : r = −3 sin(2θ) and C2 : r = 3 sin θ. 1. What is the equation of the…

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Q: Graph the sets of points whose polar coordinates satisfy the equationsand inequalities θ= 2π/3, r ≤…

A: As per the question we have to graph the sets of points whose polar coordinates satisfy the equation…

Q: Under what conditions can you find the length of a curver = ƒ(θ), a ≤ θ ≤ b, in the polar coordinate…

A: step 1 :           Conditions to find the length of the curver = f(θ) , ∝ ≤ θ ≤ B* The curve r =f(θ)…

Q: Find where the polar function f (theta) = 6 cos(theta) has a vertical tangents over [0,2pi]

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Q: Using the polar function r = 1 + cos(θ), find the slope of the tangent line at the point (3/2, pi/3)

A: Given: The polar function is, r=1+cosθ

Q: Sketch with direction of the following functions r = f(θ) in polar coordinate. please sketch with…

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Q: What quadrant does the spiral r=-theta enter first as theta increases from 0 ?

A: The equation you provided, r = -θ, describes a spiral with a negative slope. In polar coordinates, θ…

Q: Sketch the curve r = 1/2 θ (the spiral of Archimedes) for θ between 0 and 2π by plotting the points…

A: The curve is  r=12θ ;0,2π The table with the values  θ 0 π4 π2 π 3π2 7π4 2π r 0 0.392 0.785…

Q: With polar coordinates (3, -1), find (r, θ) for r>0 and r

A: The point in Cartesian co-ordinate is given by .

Q: Sketch with directio

A: Given:  Three polar coordinates. We have to sketch the graph with their directions.

Q: Write the corresponding rectangular equation for the curve represented by the parametric equations…

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Q: Consider the polar curve r = sin(30). Sketch the polar curve on the inter 0< 0 < 27/3.

A: Solution: Given data, r = sin(3theta)