Find the equation of the tangent line(s) to the following set of parametric equations at the given point. = 2 cos (3t) - 4 sin (3t) and y = 3 tan (6t) at %3=

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: Given problem is :

Q: Find the slope of the line tangent to the following polar curve at the given point. 3n r=3-3 sin e;…

A: Given polar curve is r=5sinθ. To find: The slope of the line tangent to polar curve at point 6,3π2.…

Q: Find the Cartesian equation of the curve: [2r/r2 = 1+ cos a]

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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: Find the points at which the following polar curve has a horizontal or a vertical tangent line. r= 5…

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

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

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Q: Find an equation in rectangular coordinates for the curve r^2 = cos 2θ.

A: We know that, the relationship between polar and rectangular co-ordinates are given as r2=x2+y2…

Q: Find an equation y = f (x)for the parametric curve and compute dy/dx by differentiating f (x). x =…

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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: Find the slope of the line tangent to the polar curve at the given point. 11n r= 4 sin e; - 2,-

A: Given,            r=4sinθ ; -2,11π6

Q: determine the slope of the tangent line to the polar curve r = 1+3 cos(20) at 0 6

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

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Q: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…

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Q: Find the parametric equation of the line through a = 3 A co which is parallel to b = 2

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Q: Given the curve with parametric equation x= e* and y= In(2-r²) Find the equation of the normal to…

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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: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: A polar curve is given by, r=sinθ+3cosθ. The objective is to find the slope of tangent line of the…

Q: Find the slope of the tangent line to the polar curve r = cos 20 at 0 T 3

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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: Which of the following is the equation of tangent line of the curve that is given by parametric…

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Q: Find Dx 2 y of the following parametric equations: x= cos t y= sin t

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Q: Find the graph of the parametric equations x = cos t, y = sin t. (0 ≤ t ≤ 2Π)

A: When angle increases from 0 to 2π we have increase in angle in the anticlockwise sense. Use the…

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: We use the slope of the tangent line of a curve y=f(x) to answer the given question.

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: The equation of a tangent line passing through the point x1, y1 and slope m is y-y1=mx-x1. The slope…

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

A: Given,          The parametric equation are x=5cosθ+θsinθ and y=5sinθ-θcosθ.

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: Find the points at which the following polar curve has a horizontal or a vertical tangent line. r= 9…

A: Our guidelines for multiple questions answer only first question

Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=<t+1,t,1t>=<x, y,…

Q: Find the points at which the following polar curve has a horizontal or a vertical tangent line r= 2…

A: We have r = 2 sinϴ  Take x = r cosϴ = 2 sinϴ cosϴ = sin(2ϴ)  y = r sinϴ = 2 sinϴ sinϴ = 2 sin2ϴ…

Q: Find the slope of the line tangent to the following polar curve at the given point. 3π r= 5-5 sin 0;…

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Q: Consider the following parametric curve: x(t) = 3t^2 −6 and y(t) = 3t^4 −3t^2 +12t +10 Find the…

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Q: x = 1– t- t - te [-2,2] y =t – t3

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Q: Consider the following parametric equation.  x = 14(cosθ + θsinθ) y = 14(sinθ - θcosθ) What is…

A: Given parametric equations are x=14cosθ+θsinθy=14sinθ-θcosθ

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A: Consider the equation of helix given by r(t). Find the value for t , derivative at t and modulus of…

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

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: Given,  r=9+2 cosθ

Q: Graph the parametric equations below (x(t) = 3 cost + cos 3t ly(t) = 3 sint - sin 3t

A: To graph the parametric equations.

Q: Find the derivative of the following parametric equations. (a) x = t2 + 5t + 4, y = 4t (b) x = 0 –…

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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: Find the slope of the tangent line to the given polar curve at the point specified by the value of 6…

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Q: Find the equation of the tangent line to the curve described by the parametric equation described…

A: To find the equation of the tangent to the curve described by parametric equation x=t4+2y=t3+t3,-2

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

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Q: e of the tangent line to the polar sin(40) at 6 curve r =

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Q: Find the slope of the tangent line to polar curve V3 T 3 2 r = 6 – 3 sin 0 at the point | 6 3…

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Q: Find the slope of the tangent line to the polar curve r= cos0 at 0 = T|6

A: Given data : r=cosθ  at  θ=π6

Q: For the parametric equations x = cos(t), y = 3 sin(t), find the equation of the tangent line to the…

A: Given that the parametric equations of a curve is                               x = cos (t) ,   y =…

Q: Given that r= cos 0 ; dx = - sin 20 and de dy = cos 20. do The slope of the tangent line to the…

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

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