2. a) Show that the (signed) curvature for a curve in polar coordinates (r, 0) is given by where ...
(3 points) (a) The Cartesian coordinates of a point are (-1,-V3) (i) Find polar coordinates (r,0) of the point, where r > 0 and 0 < θ < 2π. (ii) Find polar coordinates (r,0) of the point, where r < 0 and 0 < θ < 2π. Y= (b) The Cartesian coordinates of a point are -2,3) (i) Find polar coordinates (r,0) of the point, where r > 0 and 0 < θ < 2π. (ii) Find polar coordinates (r,0)...
AME: 2. (24pts) Consider the curve given in polar coordinates by r-12 cos(0) Vsin(0), (0 0 < #). (i) Make a table of the values of the function f(0)--12 cos(0)/sin(0) /6 /4 n/3 5m/12 m/2 7m/12 2n/3 3n/4 5n/6 11 m/12 f(0) are to be rounded to two decimal places. (Hint. Given on 0, r); all the values f(0) an angle 9, enter the value of 0 to the variable C of your calculator, and then evaluate /(0) using the...
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...
Find two other pairs of polar coordinates of the given polar coordinate, one with r> 0 and one with r< 0. Then plot the point. (a) (5, 5t/3) (r, θ) (r, θ) = (r>o) (r 0) (r < 0) (r 0) (r, θ) (r < 0) = Find two other pairs of polar coordinates of the given polar coordinate, one with r> 0 and one with ro) (r 0) (r
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) =
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?
(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
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I α(s) sin(θ(t)) dt Use your result to give another geometric interpretation to the (signed) curva- ture and its sign? to) rindy,R-- parmetrised with unit speed suchhat y -0and kt) - s for all seR. (a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I...
#49,53,57 3- lar coordinates to polar coordinates will Polar Coordinates Convert blar coordinates with r> 0 and the ove describe of the the rectangular con 050<27. 37. (-1,1) be app 39. (V8, V8) 41. (3.4) 38. (3V3,-3) 40. (-V6, -V2) 42. (1,-2) 44. (0, -V3) your a (a) Yo (b) YO 43. (-6,0) Rectangular Equations to Polar Equations Convert the equation to polar form. 45. x = y *.47. y = x² 49. x = 4 46. x² + y2...
Consider the polar graph r=1-sin theta and r= sin theta, shown below. Please help with B, D, and E 5. Consider the polar graphs r = 1-sin 0 and r = sin 0, shown below. a. Find the polar coordinates (r, 2) for all points of intersection on the figure. Hint: Not all points can be found algebraically. For b.-d., set up an integral that represents the area of the indicated region. b. The region inside of the circle, but...