Find parametric equations for the tangent line to the curve x=2 sin t, y= 2 sin 2t, z=2 sin 3t at the point (1, √3, 2). Graph the curve and the tangent line on a common screen.

Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

A: Obtain the equation of tangent by eliminating the parameter theta as follows.

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Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

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Q: Find the equation of the tangent line to the parametric curve at (9,2). x = t3 + 1 y = t2 - t

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Q: Show that the curve  x = 3 cos(t), y = 5 sin(t) cos(t)  has two tangents at (0, 0) and find their…

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Q: of the points where the parametric equation y = 2 cost 0≤t≤ 2π will have vertical tangent. Determine…

A: Given is the parametric equation x=5sin2t , y=2cost   0≤t≤2π We have to find the point where the…

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A: Given parametric equation is

Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…

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Q: find the inflection point to the right of y-axis of the curve defined by the equation, y=x^2/2 +…

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Q: of the points where the parametric equation y = 3 cost 0≤t≤ 2T will have a horizontal tangent.…

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Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

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

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Q: determine the slope of the tangent line to the polar curve r = 3 + 8 sin 0 at 0 =

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Q: 5. Determine the slope of the tangent line, the the equation of the tangent line, and the concavity…

A: this is the equation of tangent line.

Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

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Q: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

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Q: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: 12. Find the equation of the tangent line to the polar curve r = 2-sin(0) at 0 = 1/3. Draw.

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Q: Find the tangent plane to the equation 3y cos(5x – 4y) at the point (4,5,15)

A: z=3y cos5x-4y Let, Fx,y,z=3y cos5x-4y-z=0  ......(1) Now,  Fx=∂Fx,y,z∂x=-3y sin5x-4yx5-0…

Q: What is the equation for the line tangent to the parametric curve I = 4 sin(2t) y = 4 sin(t) at t=…

A: Explanation: Given that: x=4sin2ty=4sintt=π6or 30° Concept used: The standard equation of line…

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<π2

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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

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Q: Find the exact length of the curve. y = In(sec(x)), 0≤x≤ w|ले

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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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