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

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

A: Given:

Q: Find the exact slope of the tangent line to the 4 cos(t) parametric curve at the point ly = 7 sin(t)…

A: To Determine: Exact slope of the tangent line to the parametric curve :

Q: Find the length of the curve 7 (t) = (3 cos(t), 3 sin(t), 5t) for – 4 <t <1 Give your answer to two…

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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: Find orthogonal trajectory to the curve given by r = a(1 + cos θ)

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Q: Find the length of the curve. x = cos t y = sin t

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Q: Find the length of the curve x = e' cos(t), y = e' sin(t), 0 <t < r. Length =

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Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0 <t< n/4

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Q: Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

A: SOLUTION-

Q: Find the length of the curve. x= cos t+tsin t, y = sint-t cos t, 0sts ..... The length is units.

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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: Find the length of the curve. r(t) (7t, 3 cos t, 3 sin t), -2 sts 2

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

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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: Find the slope of the tangent to the parametric curve c(t) = (cos t, sin t) at the point (-1/2,-V3).

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

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Q: Find the length of the curve y = ln (sec x), 0&lt;= x&lt;= pai/4

A: Given,

Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

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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: 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: Find the angle between the radius vector to the curve r = 2a sin 30 and its tangent when 0 = /6.

A: The given curve is r and differentiate with respect to theta:

Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: Find the length of the curve cos(t) + In(tan(;t)), y= sin(t), n/4 <t < 3T/4. x = %3D Length = %3D

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Q: 5. R = (sin 2t , cos 2t , 2t3/2), 0 <t<1.

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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: Find the lengths of the curves x = cos t, y = t + sin t, 0≤ t ≤ π

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Q: Find the slope of the tangent line to polar curve V3 T r = 4 – 6 sin 0 at the point 4 – 6 Preview

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

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Q: Let Sketch the curve and find the length of this curve. r(t) = (t, 3 cost, 3 sin t), 0≤ t ≤ 2π.

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

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Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…

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Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

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Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: Given: x=8cost+8tsinty=8sint-8tcost0≤t≤π2

Q: Find the curva tuie For He Curve 2+); +(6 cos 2t) + 5¢ K %3D

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Q: Find the length of the curve. r(t) = (3t, 3 cos(t), 3 sin(t)), -3 sts 3

A: For the curve r(t) = f(t) , g(t), h(t)On the interval [a, b]The length is given by L =…

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

A: x=sinht,  y=cosht

Q: Find the Cartesian equation of the curve: x = 2cos(theta) y = 1 + sin(theta) where theta is…

A: Given that the equation of the curve, x=2cosθy=1+sinθWhere,  0≤θ&lt;π2

Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: Find the slope of the tangent line to polar curve r = 8 sin 0 at the point

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Q: The parametric equations of a curve are given by 2 x = In and y = cosh-(2t). when t = 1. dx Find

A: Given,            The parametric equations of a curve are given by              x=ln2t  and…

Q: Find the length of the curve r(t) = (cos(3t), sin(3t), 4t) for -6 ≤ t ≤ 5 Give your answer to two…

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Q: Find the arclength of the curve x 5 cos(8t), y : 5 sin(8t) with 0 <t <

A: Given: x= 5cos8t  ; y = 5sin8t     with 0≤t≤π8---------------------Aim: To find the arc lengthL of…

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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