Eliminate the parameter to find a Cartesian equation of the curve, and sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. 1 cos 0, 2 y = 2 sin 0,

Q: The parametric equations x= 3 - 8 sin 3t and y = 9 + 8 cos 3 t for 0 sts x/4 represent a curve C.…

A: Given data: x(t)=3-8sin(3t) y(t)=9+8cos(3t) for 0≤t≤π4 Solution: Length of parametric curve is given…

Q: Find a Cartesian equation for the curve. r2 cos(2?)

A: We have  to find cartesian equation

Q: In  the given equation as follows , sketch the curve represented by theparametric equations…

A: Curve represented by the given parametric equations & the corresponding rectangular equation by…

Q: For the plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. x- 2…

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

A: x=sinθ2 sinθ2=x θ2=arcsinx θ=2arcsinx

Q: Consider the following. x = 7 sin(6?),    y = 7 cos(6?),    0 ≤ ? ≤ pi/3 (a) Eliminate the parameter…

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Q: By eliminating the parametert, find a Cartesian equation of the curve. Draw the curve and indicate…

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Q: a) Eliminate the parameter to find a Cartesian equation of the curve. b) Sketch the curve and…

A: From x=12cosθ we get  cosθ=2xFrom y=2sinθ we get sinθ=y2Using the Pythagorean identity we…

Q: e polar equation for the curve whose rectangular(cartesian)equati 8. (b)r² . =)rcos@sine = 4 4 (c)…

A: We have to choose the correct answer from the given option according to the given condition

Q: x = 2 cos(?),    y = 3 sin(?),    −pi/2 ≤ ? ≤ pi/2 Eliminate the parameter to find a Cartesian…

A: Given that x=2 cost and y=3 sin t where -π2≤t≤π2. To eliminate the parameter ,divide first…

Q: From the information given, find the quadrant in which the terminal point determined by t lie sin(t)…

A: Given; Sin(t) < 0 and cos(t) < 0.

Q: Trace the curve r= 1/2 sin(theta) cos^3 (theta)

A: Given curve is: r=12sinθcos3θ ⇒r=142sinθcosθcos2θ=14sin2θ1+cos2θ2=18sin2θ+18sin2θcos2θ Here replace:…

Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. 9 3 cos 0+2…

A: Let's convert to Cartesian equation.

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: The parametric equations x= 8 − 6 sin 3t and y = 8 + 6 cos 3 t for 0 ≤ t ≤ π/4 represent a curve…

A: Given: Parametric equations Formula used

Q: Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate…

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Q: Change the equation to rectangular coordinates. r(3 cos e + 4 sin 0) = 12

A: r3cosθ+4sinθ=12

Q: Consider the following. X = sin A y = cos -π<θ< π (a) Eliminate the parameter to find a Cartesian…

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

Q: A bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= 4 cos 0 -8…

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Q: A bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the…

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Q: An arrow is shot upward, with an initial velocity of 85 meters per second, at an angle of 31° with…

A: When an object is thrown in air against the gravitational pull, then the motion of object is called…

Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. 4. 7 cos 0+2…

A: To convert the given equation into cartesian form.

Q: O E Clear select The slope of the given parametric equation when A- 30 degrees is equal to x = 16…

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Q: Show that r = a cos θ + b sin θ is the equation of a circle passing through the origin. Express the…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= 4 cos 0-10…

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Q: Name the type of basic curve that the following pair of equations represents: x = 2 cos(3t), y =…

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Q: The equations of the lines tangent to the equation r = 3 cos(40) at the pole r = 0 have the form 0 =…

A: Solution of this question is

Q: The parametric equations x= 4 − 6 sin 4t and y = 6 + 6 cos 4 t for 0 ≤ t ≤ π/3 represent a curve…

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

A: Explained below

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…

Q: Sketch the following curves and find the points of intersection of the pairs of curves. a) r=…

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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: Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 4…

A: (a) Determine the speed of the plane.

Q: a) Eliminate the parameter to find a Cartesian equation of the curve. b) Sketch the curve and…

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Q: TT T 9. x = sin t, y = cos 2t,

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Q: Consider the following. x = 3 cos(θ),    y = 4 sin(θ),    −π/2 ≤ θ ≤ π/2 (a) Eliminate the…

A: Calculation:(a)Compute the Cartesian equation as follows.Rewrite the equation x = 3cos(θ)  and y =…

Q: = 2/(1+ cos 0) and find its relevant parame Identify the curve r = Write an COS equivalent Cartesian…

A: We know that the Cartesian coordinate x,y of a points related to its polar co-ordinate r,θ is given…

Q: : When the axes are retated through an angle a, Find the transformed equation of x cos a + y sin a…

A: When the axes are rotated through an angle a then we have to  find the transformed equation for the…

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: х%3D cos 0, у — sec'0, 0 0< п/2

A: x=cosθ,  y=sec2θ,    0≤θ&lt;π2 a). Consider, y=sec2θ⇒y=1cos2θ⇒y=1x2⇒x2y=1

Q: From the information given, find the quadrant in which the terminal point determined by t lies.…

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

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Q: 9. The Cartesian equation of the curve r=- is 1-cos(0) (Write your answer in the following form y?=…

A: For polar form,  Substitute  r=x2+y2;cosθ=xrsinθ=yr

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

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Q: The parametric equations x= 6 − 9 sin 2t and y = 5 + 9 cos 2 t for 0 ≤ t ≤ ?/4 represent a curve C.…

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Q: Find a Cartesian equation for the curve. r = 7 sec(?)

A: Given query is to find the Cartesian equation if the curve.

Q: 2. Given the parametric equation: x= 4 cos (t), y=9 sin (t), 0 <t< 2n, a) sketch the curve and…

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Q: Consider the following. x = 9 sin?(t), y = 9 cos?(t) (a) Eliminate the parameter to find a Cartesian…

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