The graph of the equation r = 2 sin 2θ is called a four-leafed rose.
(a) Sketch a graph of this equation.
(b) Convert the equation to rectangular coordinates.
Find two polar coordinate representations of the point (8,-8). one with r > 0 and one with r < 0. and both with 0≤θ≤2π .
The graph of the equation r = 2 sin 2θ is called a four-leafed rose.
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.
Find the area of the specified region. 15) Inside one leaf of the four-leaved rose r 7 sin 2θ 16) Shared by the circles r 3 cos 0 and r-3 sin 17) Make sure you can also convert from Cartesian coordinates to polar form and find where on parametric and polar equations there are horizontal and vertical tangent lines.
Find the area of the specified region. 15) Inside one leaf of the four-leaved rose r 7 sin 2θ 16) Shared...
Convert the polar equation to rectangular form and sketch its graph. r = 7 cot(0) csc(O) Step 1 The polar coordinates (r, e) of a point are related to the rectangular coordinates (x, y) of the point as follows. x=rcos(0) cos y = r sin(0) sin e Step 2 The given polar equation can be rewritten as follows. r 7 cote csco 1 r = 7 coto sino 2 sin(0) = 7 coto Converting to rectangular coordinates using x =...
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PART II 7) (8 pts) Given the polar equation r = 6 sin θ, 0 θ π a) Graph and find the length of the graph geometrically. b) Find the length of the graph by integrating. 8.) (9 pts) Given the four-leaved rose r 2sin(26). a) Show the symmetries. b) Find the tangents of the leaf through the pole to determine the limits of integration. c) Find the area of one leaf.
PART II 7) (8 pts)...
4. Given a point (-3,-) in polar representation, answer each question. a) Plot the point b) Find two additional polar representations, using -2n< < 26 c) Convert to rectangular coordinates. 5. Convert the rectangular point (V3.1) to polar coordinates where 0 <<2 6. Given a polar equation r = 4sin e a) Sketch the graph of the polar equation by completing the table. r 0 FT/6 1/2 5/6 b) Convert the polar equation into a rectangular equation,
5. Consider the polar graphs, r = 1-sin θ and r = sin θ , shown in the figure below. Find the polar coordinates (r, θ) for all the points of intersection on the figure. a) b) Find the area of the region that lies inside both the graph of r-1-sin θ and Find the slope of the line tangent to the graph of r-1-sin θ at θ-- Find a Cartesian equation for the line tangent to the graph of...
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36. Question Details LarCalc11 10.R.065 My No The rectangular coordinates of a point are given. Plot the point -1,2) -42 -2 -2 Find two sets of polar coordinates for the point for 0 smaller 8-value r, 6)- larger 9 value)- θく2 (Round your answers to three decimal places.) 37. Question Details LaiCalc11 10.R 107 МУ Notes Use a graphing utility to graph the polar equation. common intariar of r - 4 -2 sin( and4+2 sin(0)...
you can skip question 1
Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
(1 point) Find the area of the inner loop of the Imacon with polar equation r-7 cos θ-2 =cos-1(3) Answer: (1 point) Sketch the segment r-sec θ for 0 θ Then compute its length in two ways: as an integral in polar coordinates and using trigonometry
(1 point) Find the area of the inner loop of the Imacon with polar equation r-7 cos θ-2 =cos-1(3) Answer:
(1 point) Sketch the segment r-sec θ for 0 θ Then compute its length...
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