Consider the parametric equations x = 4 cos(0) and y = 2 sin(0). (a) Create a table of x- and y-values using 0 = -n/2, -n/4, 0, t/4, and a/2. ーズ/2 ーエ/4 T/4 T/2
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- Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−8t cos(8t), y = e−8t sin(8t), z = e−8t; (1, 0, 1)Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=e^(-3t) cos (8t) y = e^-3t sin (8t) z = e^-3t (1,0,1)1. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x= e−2t cos(2t), y = e−2t sin(2t), z = e−2t; (1, 0, 1) 2. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−2t cos(2t), y = e−2t sin(2t), z = e−2t; (1, 0, 1) 3. Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 4t i + (5 − 2t) j + (1 + 3t) k
- Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point ->(5,0,0). x=5e^t, y=te^4t,z=te^(t^5)Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)
- 11. Obtain the rectangular equation from the parametric equations by eliminating the parameter t X=t and Y=2tSuppose a curve is traced by the parametric equations x= 6.08 sin(t) and y = 22 - 6(cos(t))^2-12sin(t). For what value of the parameter t, the corresponding point (x,y) is such that the curve has a horizontal tangent at (x,y)? t = ?A particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t sin 2t. Find the speed of the particle when t = /2.
- The parametric equations x = 4 - 5 sin 3t and y = 3 + 5 cos 3t for 0 ≤ t ≤ π/2 represent a curve C. Draw the curve C, indicating the direction of increasing t and then find the length L of the curve C, using an appropriate integral.Find the second derivative of y with respect to x from the parametric equations given.x = 3 + 4 sinθ , y = 3cosθ − 4Find the graph of the parametric equations x = cos t, y = sin t. (0 ≤ t ≤ 2Π)