a) Compute the enclosed area and length (from 0 to 2pi) of the parametric curve given by 3, 3, x = A sin 0 and y = A cos 0.

Q: Show that the graph of the equation r = 2a sin θ, a > 0, is acircle of radius a with center at…

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Q: Match the given parametric equations with one of the parametric curves. x=3- sint, y=3+ cost

A: It is given that x=3-sint, y=3+cost. we have to find the graph of the parametric curve

Q: By eliminating the parameter, determine the rectangular equation equivalent to the parametric…

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Q: osen y

A: Is it sen y =x

Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: Q2 - A) Find the parametric equations for the line that is tangent to the given curve : r(t) = (a…

A: To find The parametric equations for the line that is tangent to the given curve

Q: determine the slope of the tangent line to the polar curve r = 1+3 cos(20) at 0 6

A:

Q: (10) Let r(t) = (e'cos 2t, e sin 2t, e2t) a) The curve lies on a quadric surface. Give the equation…

A: Given parametric equation is  rt=etcos2t,etsin2t,e2t           (i) Let us consider…

Q: Consider curve given in polar coordinates by Find the derivative r = 8 cos 0,0 ≤ 0 ≤ π/2, dr = -8…

A: We need to find out the area of the surface of revolution formed by the given function.

Q: Consider the family of curves described by the parametric equations x = a cos t + h, y = b sint + k.…

A: The parametric equations of a curve in two variables are obtained when both the variables of the…

Q: 2.) Given the parametric equations x=cos3t and y=sin3t. Find the equation of the normal line at the…

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Q: Find the slope of the tangent line to the polar curve r=2cos0 at O %3D 4

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Q: 7. Find all points of intersection of the r= 3sine polar curves: such that r= 1+sine

A: We equate the two equation to find solutions.

Q: What is the formula for the derivative for dy/dx for a polar curve r=f(theta)?

A: Given that

Q: Find the slope of the tangent line to the polar curve 7 = 1-sin 40 at 0= 04 0- 12/12 O 5√3+4 1-4√3

A:

Q: Find parametric equations for the surface generated by revolving the curve y = 21 sin x about the…

A: The objective here is to find the parametric equation for the surface generated by revolving the…

Q: Sketch with directio

A: Given:  Three polar coordinates. We have to sketch the graph with their directions.

Q: 2 lnt and y: where 1<t<3.

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Q: Describe and sketch the parametric curve in R given by x = cos t, y = sin t, z = sin 2t

A: The general form of the parametric equation of the curve in three-dimensional space is given by…

Q: 2a) Find the slope of the curve represented by the parametric equations, at 0 = T/6 %3D x = 5+ 3 sec…

A: The curve given is  x=5+3sec θy=-3+4tan θ

Q: Consider the Lissajous figure given by the set of parametric equations cos(5t), y = sin(3t). Select…

A: Topic = Derivative