What type of limaçon is graphed by the polar equation r-4 + 2 sin θ ? Identify the axis of (4 points) symmetry and horizontal and vertical intercepts What type of limaçon is graphed by the polar...
If a curve whose polar equation is r-r0) is rotated about the pole though an angle φ, then an equation for the rotated curve is r " no- Write an equation for the limeçon「-4-sin θ after it has been rotated counterclockwise by the given amount. Uso a graphing utility to graph the rotated limaçon for θ m/4, θ-n/2, θ π, and 3a/2. (Match the rotation to the correct graph.) (a) θ π/4 rotation r- graph (b) /2 rotation r- graph...
3. (18 points) Consider the polar equation r = 2 + 2 cos(0). Describe the graph of this equation. What is it's axis of symmetry? How would you change the equations to make this a limaçon with an inner loop?
Identify Symmetry in Polar Equations and Curves Question Based on the results of a test for symmetry, which of the following equations demonstrate polar axis symmetry? Select all that apply. Select all that apply: r-sin +2 COS 4sin20-5cos205 Identify Symmetry in Polar Equations and Curves Question Based on the results of a test for symmetry, which of the following equations demonstrate polar axis symmetry? Select all that apply. Select all that apply: r-sin +2 COS 4sin20-5cos205
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...
6) Identify the vertex, axis of symmetry, and intercepts for the graph of the function. 6) g(x)=x2- &x + 7 A) Vertex at (4, -9); axis: y = -9; x-intercepts: none; y-intercept: (1,0) B) Vertex at (-4,55); axis: x=-4; x-intercepts: none, y-intercept: (1,0) Vertex at (-4,55); axis: y = 55; x-intercepts: (1, 0) and (7,0); x-intercept: (0,7) D) Vertex at (4, -9); axis: r = 4; x-intercepts: (1,0) and (7,0); p-intercept: (0,7)
1. The polar curves r@) = 1 + 2 sin(39), r = 2, are graphed below. 2 (a) Find the area inside the larger loops and outside the smaller loops of the graph of r 12 sin(30). [Hint: Use symmetry, the answer is 3v3.] [Answer: sf-i.] quadrant where r is maximum? (b) Find the area outside the circle r 2 but inside the curve r 1+2 sin(30) (c) What is the tangent line to the curve r-1+2sin(30) at the point...
Find the points of horizontal tangency to the polar curve. r = a sin ose<, a > 0 (r, 0) = (smaller r value) (r, 0) = (larger r value) Find the points of vertical tangency to the polar curve. (r, ) = (smaller e value) (r. 2) = (larger e value)
3. Determine the equation of the function graphed to the right: [3 Points) YA 20 16H 12 8H 4 (1,5) (0.1) f(x) = -3 2-1 1 2 3y=0 4. Determine whether the following are symmetric about the x-axis, y-axis, and/or origin. Answer 'Yes' or 'No' to each prompt below. [6 Points) b) x = y2 +3 3+ 2- 1- 4-3 -2 -1.11 1 2 3 -2- -3 x-axis Symmetry? x-axis Symmetry? y-axis Symmetry? y-axis Symmetry? Symmetry about origin? Symmetry about...
Replace the Cartesian equation y = 19 with an equivalent polar equation Question 1 The equivalent polar equation is (Type an equation using rando as the variables. Type an exact answer, using t as needed.) Graph the curves r= 2 + 4 cos 0 and r= 2 + 4 sin 0. Question 2 Identify the correct sketch of r= 2 + 4 cos 0. OA. OB. O c. OD -8 pi -8 Identify the correct sketch of r= 2 +...
I need the area between the loops 4 points | Previous Answers LarCalc9 10.5.022 e a graphing utility to graph the polar equation. r-8(1 + 2 sin(θ)) 2아 15 WebAssign Plot 10 10 O 10 5 4 points | Previous Answers LarCalc9 10.5.022 e a graphing utility to graph the polar equation. r-8(1 + 2 sin(θ)) 2아 15 WebAssign Plot 10 10 O 10 5