Given this pair of parametric equations and interval for t, x=t+sint, y=cos(2t), 0 ≤t ≤2 (A) write out the first derivative in simplified form. (B) at what values of t does the graph have a horizontal line? (C) what are the ordered pairs at the horizontal tangent lines?

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A: We have to eliminate the parameter and find the cartesian equation.

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

A: Explanation :  Given that x= 3cost + sint y = e^2t

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A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

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A: Given: x=4 costy=2 sin2tt=π3

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A: Given query is to find the Cartesian equation.

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A: Given that: x=2-3cosθ and y=3+2sinθ

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Q: 1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that

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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…

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

A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…

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

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A: Given: x=t-sint y=1-cost at t=pi/3

Q: Can the parametric curve (t, sin t) be represented as a graph y = f (x)? What about (sin t, t)?

A: Parametric curve is (t, sint) i.e x = t and y = sint

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

A: x=sin12θ,  y=cos12θ

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Given, the surfaces:               x+y2+2z=4,   x=1  Point: (1, 1, 1) Let         z = 1-2t

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A: The given parametric equations of the particle is dxdt=-2t sin2t and dydt=2t cos2t. Evaluate the…