a. Consider the curve in the plane given in polar coordinates by r= 4sin 0. Find the carte- sian equation for the curve and identify the curve. b. Consider the region D in the first quadrant of the ry-plane, bounded between the curves whose polar equations are r = 4 sin 0 and r = 5. (1) Sketch the region, label axes and intercepts and set up the integral ,r dA in polar coordinates. You need not evaluate. (ii) Set up the integral , r dA in rectangular (cartesian) coordinates; you may have to use a sum iterated integrals, and you are free to decide which ordering to use. You need not evaluate.

Q: Sketch the polar curve r = 2 − 2 cos(θ). can you please show how you found all the points necessary…

A: In the question it is asked to draw polar curve for function r=2-2cos(θ).

Q: 4. D is the region in the first quadrant which is bounded by the circle x² + (y-1)² = 1 and the…

A:

Q: Given the polar curves: C1: r = 1+sinθ and C2: r = 3sinθ, I.   determine the curves' intersection…

A: For polar curves r1=f1(θ) and r2=f2(θ) such that r1>r2, in the limits θ=α to θ=β, the area…

Q: H.W : Sketch the curve r 0 in polar coordinates for: i. (0 <= 0) ii. (- 0 < 0 < ∞)

A: A polar coordinate system contains a reference point and a reference direction. The reference point…

Q: Find the rectangular coordinates (x, y) that describe the image of the point with polar coordinates…

A:

Q: Find the angle α between the polar curves r1=eθ and r2=e−θ at the point of intersection.

A:

Q: Sketch the polar curve 0=1

A:

Q: 1.5 -1 X X 3 1.0 0.8 0.6 0.4 0.2 1 2 3 X

A:

Q: 3. Let (x, y) denote the usual rectangular coordinates. Write the following function f(x, y) in…

A:

Q: Given the polar curves: C1: r = 1+sinθ and C2: r = 3sinθ, I.   determine the curves' intersection…

A: Given: The polar curves: C1: r=1+sinθ and C2:r=3sinθ To find: I.   The curves intersection points in…

Q: Sketch the curve r = 8+8cos € in polar coordinates.

A:

Q: Q5/ Consider the following polar curves r = 2 - 2cos0 and r 5+2cose 1. Graph the above equations in…

A: For the range 0≤θ≤2π, construct a table of values for both curves followed by graphs of each, as…

Q: Sketch the graph of r = θ (θ ≥ 0) in polar coordinates by plotting points.

A: Consider the given curve. r=θ   (θ≥0)

Q: Use the two polar equations r=-6*cos(theta) and r=6 - 6*cos(theta) to answer parts a through b a.…

A:

Q: 6. Find a Cartesian equation for the polar curve and describe its shape: r= 3csce

A: The given equation,              r=3 cscθ

Q: rl+ 4sino

A:

Q: Plot the following curves in polar coordinates. 4. r r = sin() 5. r= 1 + cos 50 6. r² - sin 0

A:

Q: Sketch the curve given in polar coordinates. r = 2 + 4sine , 0 < 0 < 2n

A: Consider the polar curve  r=2+4sinθ                             0≤θ≤2π

Q: For the polar equations r1=1-cosx and r2=1, (1)sketch the graphs of r1 and r2 in the same coordinate…

A:

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)

Q: Does the origin lie on the polar curve r = 1 – 3cose ? Explain.

A: We will first plot the polar curve in the 2D (r,θ) plane with polar coordinates. We shall plot it…