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- Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.Suppose 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 = ?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 the equations of the lines tangent and normal to the curve given by the parametric equations x = 4 cos t and y = 2sin2 t at t = π/3Eliminate the parameter t from the parametric equationsx = 3+1 2 sec t and y =2+ 4 tan t.11. Obtain the rectangular equation from the parametric equations by eliminating the parameter t X=t and Y=2t
- Find parametric equations for the tangent line at the point(cos(−4π/6),sin(−4π/6),−4π/6) on the curve x=cos(t), y=sin(t), z=(t) x(t)= y(t)= z(t)=Suppose a curve is traced by the following parametric equations as t runs from 0 to pi. x=5(sin(t)+cos(t)) y=54−20cos2(t)−40sin(t) At what point (x,y) on this curve is the tangent line horizontal?3. Find the second derivative for the following set of parametric equationsa. x = sqrt(t) , y = 2t +4b. x = sec t , y= tan t
- 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)Show that cos21θ=cos^3(7θ)−3cos7θsin^2(7θ )and use this identity to find an equation in rectangular coordinates for the curve r=3cos21θ =(x^2+y^2)^2I am confused on how to find the parametric equations for the tangent line to the attached curve r(t) at the point (1,0,1)