The parametric equations x = 4 - 5 sin 3t and y = 3 + 5 cos 3t for  0 ≤ t ≤ π/2  represent a curve C. Draw the curve C, indicating the direction of increasing t and then find the length L of the curve C, using an appropriate integral.

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

A:

Q: Find the length of the curve r = cos(f) + sin(0), 0sOs

A: The objective is to find the length of the curve.

Q: Find the length L of the curve R(t) = -2 cos(5t) /+2 sin(5t) /+ tk over the interval [3, 6]. L =

A:

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

A: We have to find the length of curve.

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: 7. Find the length along the parametric curve defined by v(t) = (t, In(cos(t))) from t = 0 andt=.…

A:

Q: 2. Write an integral expression to represent the length of the path described by the parametric…

A:

Q: Find the length of the curve r = 4 cos 0

A: Given curve is r=4cosθ We have to find the length of the given curve. The length of the curve in…

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

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

A:

Q: Consider the curve C shown in the figure, parameterized by: C: r(t) = (1 - cos(t), 1- sin(t), 1 +…

A:

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

A:

Q: Given parametric equations x = 2 cos 0 and y = sin 0. d²y Then dx2 in the point (V2,) is

A: Given parametric equation is  x=2cosθ and y=sinθ

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Find the length of the hypocycloid defined by the equations x = a cos° (0), y = a sin° (0), 0 < 0 <…

A: Here we have to find the length of the hypocycloid defined by the equation x=acos3(θ) , y=asin3(θ)

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

A:

Q: 3. Find T (t) and a set of parametric equations for the tangent line to the helix given by ř(t) = 2…

A:

Q: A curve is defined by the parametric equations: x(1) = e' cos t, y(t) = e' sint d²y dy and dr of the…

A: It is given that, x(t)=et cost,y(t)=et sint   It is known that, dydx can be found by chain rule and…

Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

A:

Q: Find all the values of t where the tangent line to the parametric curve is horizontal or vertical.…

A:

Q: A curve is defined by the parametric equations (t) = 8 cos(6t) and %3D y(t) 4 sin(-4t). Find . %3D

A: We have to find derivative

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

A: Parametric equations for a line:

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: Consider the following parametric equation. x = 7(cos 0 + 0 sin 0) y = 7(sin 0 – 0 cos 0) 11 What is…

A:

Q: Given: smooth curve C parametrized by Ř(t) = 8. Cos tv2 8 sin 3 1. Find the unit tangent, unit…

A: Given

Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: 1. Consider a fence whose base is the path with parametric equations |x(t) = cos³ t, |y(t) = sin³t,…

A: Given, A fence whose base is the path with parametric equations xt=cos3tyt=sin3t for 0≤t≤π2. Let the…

Q: 1 Consider the curve defined by the parametric equations x = ÷ť & y=÷ť for 2<t<3 2 3 Determine the…

A: take derivative

Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t) j + 4ln(cos(t)) k,  0 ≤ t ≤ ?/4

A:

Q: Find the equation of the tangent line(s) to the following set of parametric equations at the given…

A:

Q: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

A:

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

A: In this question we have to find the length of the curve.

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A:

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

A:

Q: Find the length of the curve over the given interval. =8 r = 7(1+ cos 0), 0 <0< 2n

A:

Q: Find all the values of t where the tangent line to the parametric curve is horizontal or vertical.…

A: x=32t-cos tdxdt=32+sin tvertical tangent line:dxdt=032+sin t=0sin t =-32t=2nπ+4π3  and t=2nπ+5π3,…

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: 1 Find the area of the surface generated by revolving the curve x = cos (3t), y 3+sin (3t) on 0sts…

A:

Q: Find all the values of t where the tangent line to the parametric curve is horizontal or vertical.…

A:

Q: Suppose you know that the curve C is given by the parametric equations x=t+sin (t) y=cos(t) where…

A:

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

A:

Q: Consider the following parametric equation. x = 3(cos 0+ 0 sin Ø) y = 3(sin 0 -0 cos 0) What is the…

A:

Q: The length of the curve y = In(cos x), 0< x <:

A: To determine the length of the curve, y=lncos x, 0≤x≤π4.

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

A:

Q: Find the length of the parametric curve x = sin-1t,y = In V1– t² for 0 <t<-

A:

Q: 3. Find the exact length of the parametric curve x = sin-1t, y = In /1 – t2, 0<t<

A:

Q: The area of the rotational surface resulting from rotating the arc of the curve x=cos^3 t, y=sin^3 t…

A:

Q: The position of a particle in the xy-plane at time t is given by r(t) = (cos 2t) i+ (2 sin 2t) j…

A: Given: rt=cos2ti+2sin2tj For finding equation in x and y whose graph is the path of the particle, we…