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Test for symmetry about pole, polar axis, and the line theta = pi/2
r^2=2 sin 3 theta ( show work)
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- Based on the image attached, find the:- a) area, b) length of a polar curve. *Help me solve this question with step-by-step solution. Thank you in advamce.Use a graphing utility to graph the curve represented by the parametric equationsHypocycloid: x = 3 cos3 θ, y = 3 sin3 θ . Indicate the orientation of the curve. Identify any points at which the curve is not smooth.Prove that both polar curves are symmetric with respect to the polar axis. Find the polar coordinates of the points of intersection of the two polar curves. At the point where theta = pi/3, determine the slope of the tangent line to C2. Set up (but do not evaluate) the integral that gives the area and the perimeter of the region R.
- Convert the polar coordinate (6, 5pi/6 ) to Cartesian coordinates. X= Y= *Please explain your work and also make work readable* thanks!Use a graphing utility to graph the polar equation over the given interval. Use the integration capabilities of the graphing utility to approximate the length of the curve. r = 2 sin(2 cos θ), [0, π]Tangent line at the origin Find the polar equation of the line tangent to the polar curve r = 4 cos θ at the origin. Explain why the slope of this line is undefined.
- Sketch the polar curve r = 2 − 2 cos(θ). can you please show how you found all the points necessary to sketch this curveHow do you know the region in polar coordinates? How to find the polar coordinates?Multiple tangent lines at a pointa. Give the smallest interval [0, P] that generates the entire polar curve and use a graphing utility to graph the curve.b. Find a polar equation and the slope of each line tangent to the curve at the origin. r = cos 3θ + sin 3θ