Plot the cissoidr 2 sin 0 tan 0 and show that its equation in rectangular coordinates is x3 y2 2 - x

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: 4. Use the Arc Length in Parametric Form formula to find the arc length of the curve with the given…

A: Given parametric equations, x= 3sint ,   y=3cost,     0≤t≤π3

Q: The equation of the tangent line to the parametric equations, x = sine, y= 20 + cose at 0 = 0 is y =…

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Q: Find parametric equations for line that is tangent to the curve x=cost, y=sint, z=t at the point…

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Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Find the area of the surface obtained by rotating the curve of parametric equations x = 10 cos³ 10…

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Q: A cantilever beam of length L is embedded at its left end. Find the deflection of the beam when w(x)…

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Q: By using polar coordinate method, solve the double integral: 1-x x² + y? dy dx

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Determine the x - y coordinates 5 sin²t of the points where the parametric equation y=2 cost 0≤t≤ 2π…

A: The curve has horizontal tangent where the slope is 0

Q: Find the arclength of the curve a = 8 cos(3t), y = 8 sin(3t) with 0 < t<. 9

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Q: Find the cartesian equation of the curve x = 2 sin (2t) and y = 3sin (t). Graph.

A: To find the Cartesian equation of the given curve.

Q: Find the equation of the tangent line of the parametric equations x = 2 – 3 cos 0, y = 3+2 sin 6 at…

A: Given that: x=2-3cosθ and y=3+2sinθ

Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…

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Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

Q: Find the equation of the tangent line to the parametric curve x = θ+cosθ, y=1+sinθ; θ = π/6

A: We have to find equation of tangent line to the parametric curve at θ=π6 where parametric curve is:…

Q: Determine the x - y coordinates of the points where the parametric equation x = 3 sint y = 3 cost…

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Q: Find parametric equations for the tangent line at the point (cos(−4π/6),sin(−4π/6),−4π/6) on the…

A: Given parametric equation of given curve is x=cos(t), t=sin(t), z=t Differentiate with respect to t.…

Q: find parametric equation (cartesian) for tagent line to r=cos(2theta) at theta=2

A: The equation of the tangent line is

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

Q: Write an equation in general form of the tangent plane to the surface x^2+siny + z^3 = −4 at the…

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Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x = 74…

A: given curves x2+z2=74 , y2+z2=74 , point 5,-5,7  to find parametric equations for the tangent line…

Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

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Q: Sketch the parametric curve at R* whose parameterization is given by a (t) = (cos (t), sin (1), t),…

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Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…

A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…

Q: Sketch the regions enclosed by the given curves. y = 2 cos(5x), y 2 sin(10x), x = 0, x = 1/10 2.0…

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Q: Sketch the motion of a particle with position as: x = 5 sint y = ²/-nstsn - St≤n as tvaries in the…

A: We need to plot the motion of the particle, whose position is defined as: x=5sint, y=t2 in the…

Q: The unit circle x² + y = 1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

A: The unit circle can be written in parametric form as x=cosθ and y=sinθ We have to find dydx and the…

Q: The equation for the tanget to graph of y=sin^1(x/2) at the origin is

A: Given, y=sin1x2 Differentiate the given function with respect to x we get, dydx=cosx212 At point…

Q: of the points where the parametric equation y = 3 cost 0≤t≤ 2T will have a horizontal tangent.…

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Q: Find the Sufface arca 0f the soid of revolution Obtained bu rotatig y=+2x With TtxE2 around メーaxis、…

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Q: Find parametric equations for the arc of a circle of radius 7 from (0,0) to Q = (14,0). æ(t) y(t)…

A: Given that  Radius of circle is 7  P(0,0)to Q(14,0) To find the parametric equations of the circle

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ vt, y = e at the…

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Q: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

A: x=sin12θ,  y=cos12θ

Q: ..... The area of the surface generated by revolving the curve x = 1 cos (2t), y = 7+ -sin (2t) on…

A: Follow 2nd and 3rd step.

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1,л,0).…

A: Given :x=sin3ty=2tz=cos3tpoint -1, π, 0

Q: Find the slope of the line tangent to the following polar curve at the given point. 3x r= 3-3 sin 0;…

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Q: Sketch the curve by using the parametric equation to plot points. Then, eliminate the parameter 0,…

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Q: Find the points (x,y)at which the polar curve r=1+sin(θ), −π/4 ≤θ≤π/4  has a vertical and horizontal…

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Q: Determine the speed (in meters per second) of a particle with a trajectory (2 sin (3t), 9 cos (3t)),…

A: Consider the given parametric equation of the trajectory of the particle, 2sin3t,9cos3t so we can…

Q: Find the second derivative of y with respect to x from the parametric equations given. x = 3 + 4…

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Q: Use the parametric equations of an ellipse x= 9 cos e = 14 sin 0 0<0 < 2T to find the area that it…

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Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the…

A: Given polar equation is r=3cosθ

Q: Find the arc length of the curves x = e-20 (sine + cos0), y = e-20 (sine – cose) over the interval…

A: Definition used -                    Length of the curve…

Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

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Q: Find the derivative dydx of the polar function r=sec(2θ) at θ=π4

A: