AME: 2. (24pts) Consider the curve given in polar coordinates by r-12 cos(0) Vsin(0), (0 0...
NAME Q2. (24pts) Consider the eurve given in polar coordinates by 11 sin(0)Veos(). (-/ 2 < e</2) . r 6) Make a table of the values of the function f()- 11 sin(0) /co0) -Se/12)-/3-/4 6-/12 /12 | /6 /4 /3 | 5/12 -/2 tatwatwlaat on 1-r/2./2: all the values f(0) are to be rounded to two decimal places, (Hint. Ciaen an angle 0, enter the value of to the variable C of your caleulator, and then evaluate f(e) using the...
1 2 NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...
just make circle questions which 2,(b) and 3,(i) thank you 2. (Polar Coordinates: Polar Plots). (a) Consider the curve given in polar coordinates (i) Use a scientific calculator to fill in the following table with the (approximations of) values of the function r(0) on π, π r(e) (the approximations of the values r(e) must be good to at least two decimal places). (i) Use the graph paper for the polar coordinate system (attached to the assignment sheet) to plot the...
2. a) Show that the (signed) curvature for a curve in polar coordinates (r, 0) is given by where ro denotes do Hint: derive the formulas r-r(0)cosa, y-r(θ)sin θ with respect to θ b) Compute the signed curvature for the cardioid r(0) 1-sin θ Sketch the curve with a suitable plotting tool. 2. a) Show that the (signed) curvature for a curve in polar coordinates (r, 0) is given by where ro denotes do Hint: derive the formulas r-r(0)cosa, y-r(θ)sin...
A curve in polar coordinates is given by: r = 9 + 2 cos θ Point P is at θ = 20π/18 (1) Find polar coordinate r for P, with r > 0 and π < θ < 3π/2. (2) Find cartesian coordinates for point P (3) How may times does the curve pass through the origin when 0 < θ < 2π?
A polar curve r = f() has parametric equations x = f(0) cos(8), y = f(0) sin(8). Then, dy f() cos(0) + f (0) sin(e) d/ where / --f(8) sin(0) + / (8) cos(8) do Use this formula to find the equation in rectangular coordinates of the tangent line to r = 4 cos(30) at 0 = (Use symbolic notation and fractions where needed.)
(2) Let x-r cos θ, y-r sin θ represent the polar coordinates function f(r, θ) : R. R2, Compute f, (r$) and f, ( ompute * T (2) Let x-r cos θ, y-r sin θ represent the polar coordinates function f(r, θ) : R. R2, Compute f, (r$) and f, ( ompute * T
The Cartesian coordinates of a point are given. (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) =
7) The graph of r = Sin 2θ is given in both rectangular and polar coordinates. Identify the points in (B) corresponding to the points A-I in (A), with corresponding intervals.8) Describe the graph of: r = a Cos θ + b Sin θ 9) Write the equation, in polar coordinate, of a line with (2, π/9) 5 the closest point to the origin.
(a) Find the points on the polar curve r = 2(1 – cos(0)) where the tangents are horizontal. (b) Find the points on the polar curve r = 2(1 - cos(0)) where the tangents are vertical. (c) Find the length of the curve. FIGURE 3. r = 2(1 - cos(O)).