Eliminate the parameter t from the following. x = 3 + sin t, y = 5 + cos t Sketch the graph of the plane curve.

Q: Suppose the curve C is given by the parametric equations x=1+ \t y=e' where t> 0. Find a equation of…

A: The equation of tangent line to the curve is given below

Q: Consider the following. X = sin y = os(플e), -π sθ<π (a) Eliminate the parameter to find a Cartesian…

A: As we know that the trigonometric identities:- cos2(θ)+sin2θ=1

Q: Consider the following trajectory of a moving object. Find the tangential and normal components of…

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Q: Consider the following. x = sin(t),    y = csc(t),    0 &lt; t &lt; π/2 (a) Eliminate the…

A: x(t) = sin(t)y(t) =csc(t)

Q: Consider the following. tan2(0), y = sec(0), -n/2 < 0 < t/2 X = (a) Eliminate the parameter to find…

A:

Q: Consider the following parametric equation.  x = 18(cosθ + θsinθ) y = 18(sinθ - θcosθ) What is…

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Q: Suppose an object moves in an elliptical orbit parametrized byx = 4 cos t and y = 7 sin t, where t ≥…

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Q: Consider the following parametric equation. x = 5(cos 0 + 0 sin 0) y = 5(sin 0 – 0 cos 0) What is…

A:

Q: Consider the following. x = sinh(t),    y = cosh(t) (a) Eliminate the parameter to find a…

A: a) We are going to use the identity to eliminate t. Then plug x = sinh(t),    y = cosh(t)

Q: The plot above is created with the parametric equations x(t) = a cos(bt) lylt) = c sin(dt) To…

A: the given equations are as we can see here the domain of x is [-3,3] and the maximum value of x is…

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

A: The equation of a line can be obtained by using the expression y-y1=m(x-x1). Here, m is the slope of…

Q: 3) Find the length of the curve r= cos (0/3), 0< 0 <"/4:

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

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Q: • Graph the cardioid r a(1 + cose), a <0? • Graph the cardioid r = a(1+ sin6), a < 0? Graph the…

A: Graph are given below:

Q: Find the lengths of the curves 1.The curve r = cos^3 (u/3), 0&lt;= u&lt;= pai/4 2. The curve r =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Eliminate the parameter t from the following. x = 4 sin t, y = 4 cos(t) Sketch the graph of the…

A: The given question has been solved in detail

Q: Eliminate the parameter to find a Cartesian equation of the curve, and sketch the curve and indicate…

A:

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

A:

Q: Given the parametric equation of a curve: x(θ) = sin θ − 1 and y(θ) = θ + cosθ a. Find dy/dx b. Find…

A: Given that  x(θ) = sin θ − 1 and y(θ) = θ + cosθ To determine the  Find dy/dx b. Find d2y/dx2   c.…

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 the length of the curve. r(t) = , −4 ≤ t ≤ 4

A: The length of the curve is given by  r(t) = &lt;5t, 3 cos(t), 3 sin(t)&gt; r'(t) = &lt;5, -3…

Q: Consider the following. x = sin(@), y = cos(@), osesT (a) Eliminate the parameter to find a…

A: Recall: sin2θ + cos2θ=1

Q: Consider the following. x = sin(0), y = cos(0), (a) Eliminate the parameter to find a Cartesian…

A:

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

A: Given parametric equation is

Q: Consider the following. x = sin(10), y = cos(0). (a) Eliminate the parameter to find a Cartesian…

A: Given problem:- x=sin(θ/2) , y=cos(θ/2) , -π≤θ≤ π  Eliminate parameter and find Cartesian equation…

Q: Which of the following is the equation of the tangent line to the polar curve r = sec at the point 6…

A: Given,r=sec θ2At θ=π3,r = 23

Q: What curve is represented by the following parametric equations ? x = sin(t) ; y = cos(2t) ; 0 ≤ t ≤…

A: x = sin(t) ; y = cos(2t) We need to represent the curve determined by the given parametric…

Q: I thought that since (tan x)^2 + 1 = (sec x)^2, I could use that 1 = (sec x)^2 - (tan x)^2. But I…

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Q: Consider the following. x = tan2(0), y = sec(0), - T/2 < 0 < T/2 (a) Eliminate the parameter to find…

A: Explained below

Q: The astroid curve below is defined by the parametric equations x(t) = 2 cos' t, y(t) =2sin't.…

A:

Q: Consider the following. x = 4 sin(80), y = 4 cos(80), 0sos (a) Eliminate the parameter to find a…

A: Solution: x=4 sin (8θ)y=4 cos(8θ)  ,     0≤θ≤π4 Let 8θ =t  So,   0≤θ≤π4 multiplying by 80≤8θ≤8π4…

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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: Consider the following. X = 7 cos(0), y = 8 sin(0), - T/2 < 0 S TT/2 (a) Eliminate the parameter to…

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric equation is x=cos 2t,   y=sin t,    -π≤t≤π. This implies that, x=cos…

Q: Question 10. Find the angle between the curve r(t) = (t, sint, cos t), and the curve y + z2 = 1, x =…

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Q: x = 4 cos t and y = 4 sin t 0sts 4

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Q: Find the exact length of the portion of the curve shown in blue. r=2 cos²(0/2)

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Q: Consider the following. x = sin(t), y = csc(t), 0 <t< n/2 (a) Eliminate the parameter to find a…

A:

Q: Consider the following. x = sin(0.5θ),    y = cos (0.5θ),    −π ≤ θ ≤ π (a) Eliminate the parameter…

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

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Q: A parametric curve has the equations x =t+sin t and y= cos t. Calculate and , both evaluated at t=…

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

Q: Consider the following. x = sin coso), -n s 0 sa co). (a) Eliminate the parameter to find a…

A: Our objective to find the cartesian equation of the curve.

Q: Eliminate the parameter t from the following. x = 2 sec t, y = 2 tan t   Sketch the graph of the…

A: Given,           x=2sect and y=2tant

Q: Consider the following. X = sin y = = COS (a) Eliminate the parameter to find a Cartesian equation…

A:

Q: Given x= sin 0, y = cos 0, n <o< 2n a) eliminate the parameter to find the rectangular equation of…

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Q: The parametric equations x = 4 - 5 sin 3t and y = 3 + 5 cos 3t for  0 ≤ t ≤ π/2  represent a curve…

A:

Q: Consider the following. x = tan?(0), y = sec(e), -1/2 < e < n/2 (a) Eliminate the parameter to find…

A: x=tan2(θ) and y=sec(θ) knowing that tan2(θ)=(tan(θ))2=sin2θcos2θ and that…

Q: Consider the following parametric equation. x=7(cos(t) + tsin(t)) y=7(sin(t) - tcos(t)) what is…

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

A: Consider the given information. x=20cosθ+θsinθy=20sinθ−θcosθ The formula of length of the curve in…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.