Consider the curves:r = 4sin 0 and r = 2 sin(0) + 2cos (0).

Q: ) Write the equation r2+r(sin 0-6 cos 0) = 0 in Cartesian coordinates and identify the corresponding…

A: Solution is given below:

Q: The x- intercept of the tangent line to the polar curve r=(1+sin 0) at 0=" is

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Q: Show that the curves r = a sin 0 and r = a cos 0 intersect at right angles.

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Q: Consider the parametric equation x = 13(cos(theta)+theta(sin(theta)),  y =…

A: To find the length of parametric curve on [0,9π/4]

Q: Describe the shape of the curve x = 3 cos t, y = 3 sin t .

A: Given:

Q: Find the equation of the plane perpendicular to the curve r(t) = (sin(2t), t, cos(2t)) at the point…

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Q: Consider the curve defined by the parametric equations: x=5t cos t at t = t y= 5t sin t Find the…

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Q: A curve is defined by the parametric equations a(t) = 2 cos(5t) and y(t) = -7 sin(-10t). Find .

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Q: Find the expression for the tangent slope dy/dx for points on the Polar curve r= 6 +12 cosθ

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Q: 4. Convert to rectangular coordinates and sketch the curve x = 4 sec 0 y = 3 tan 0

A: Here we convert parametric equation in rectangular equation. And then we draw the graph.

Q: Sketch the curve with parametric equations x = sin t y = sin2t

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Q: Sketch the curve and Find the length if the curve: x=cos(2t), y=sin(2t), 0<_t<_ pi/2

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Q: dy Find for the curve 49 + 6x° = 3 + sin(7x-y). da

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Q: Find the slope of the tangent line to polar curve r = 6 – 9 sin 0 at the point (6-

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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 exact length of the curve r = sin 0 + cos 0.

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Q: Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0,…

A: The curve is r(t)=a cos3ti + a sin3tj   Interval is 0, 2π

Q: Find the length of the curve r(t) = (cos 3t, sin 3t, 2t3/2),0 sts 3. %3D

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Q: Determine the slope of the tangent line to the polar curve r = 1 + sinθ at θ = π/4.

A: Explanation: Given that,  r=1+sinθat θ=π4     Concept used: To determine the slope of the tangent to…

Q: Consider the parametric curve defined by x = 2020 cos t y = 2020 sin t π Find the slope of this…

A: Slope of a curve at some point is the value of the derivative at that point.

Q: A curve is defined by the parametric equations sin z dz, CoS Z dz, t 2 1. y= X= Find the length of…

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Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: The curves r₁(t) = (5t, t², t3) and r₂(t) = (sin(t), sin(5t), 4t) intersect at the origin. Find…

A: see my solution below

Q: Consider the curve given by the parametric equations x = sin t, y = sin(t + sint) where -oo <t < ∞.…

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Q: Sketch the curve y=sin(x)/(1+cos(x)).

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Use the arc-length formula of the parametric equation and evaluate the arc-length of the curve while…

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Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = sin2(t), y =…

A: Given parametric equation is

Q: Locate the center of the curve r = 4(sinθ + cosθ)

A: NOTE: Refresh your page if you can't see any equations. . the given curve is ...............(1)

Q: Find the arclength of the curve over the given interval. (a) r = 1 + sin θ, 0 ≤ θ ≤ 2π

A: Given: The curve is: r=1+sinθ over the interval 0≤θ≤2π The objective is to find the arclength of 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: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = 2 cos(t), y =…

A: Given parametric equations are

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the…

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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: The curves r1(t) = (3t, t2, t) and r2(t) = (sin(t), sin(5t), 5t) intersect at the origin. Find their…

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Q: determine the slope of the tangent line to the polar curve r = 3 + 8 sin 0 at 0 =

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Q: Find parametric equations for the line tangent to the helix r(t) =(sqrt(2)cos t)i + (sqrt(2) sin t)j…

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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: Find the slope of the tangent line to the polar curve r = sin(20) at 0 =

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Q: Find all points of intersection of the curves r = sin 0, r= sin 20

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Q: Consider the parametric curve x = sint + cos t, = cos² t 0 <t < 2n п Find an equation for the…

A: We find dx/dt and dy/dt from the given equations

Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

Q: Consider the curve y = – In|cos(x)| as x travels from T to 6 a) Find the length of the curve.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

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: A curve is given by parametric equations x = cos't and y= sin' t . dy d²y Find and in terms of t. dx…

A: dy/dx=(dy/dt)/(dx/dt)

Q: For the curve with parametric equations x = 4 sin (t) – 1 y= 2 cos (1) + 3 dy find the point dx at…

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Q: Sketch the curve r= cos 2θ

A: Symmetric test for polar coordinates r=f(θ): If f(θ)=f(-θ) then graph is symmetric about polar…

Q: At what points does the curve 2a cos t - a cos 2t, y = 2a sin t – a sin 2t x = ave vertical or…

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