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Q. Calculate the arc–length of catenary γ(t) = (t, cosh t) starting at the point (0, 1).
Q. Calculate the arc length of catenary γ(t) = (t, cosh t) starting at the point (0, 1).
Q. Calculate the tangent vectors of the following curves:
(i) γ(t) = (cos^2 t, sin^2 t)
(ii) γ(t) = (e^t, t^2)
Q. Find the cartesian equations of following parametrized curves:
(i) γ(t) = (cos^2 t, sin^2 t)
(ii) γ(t) = (e^t, t^2)
Q.Find the length of the astroid x=acos^3 t, y=asin^3 t, [0, 2π].
Q. Find parametrisations of following level curves
Y^2-x^2=1, x^2/4+y^2/9 =1
Q. Find parametrisations of following level curves
Y^2-x^2=1, x^2/4+y^2/9 =1
Q. Is γ(t) = (t2, t4) a parameterization of the parabola y=x2?
If the length of both bases and the overall height of an Isosceles Trapezoid is known, is there a formula to determine the interior angles of the shorter base? I know that both angles will be the same. (need to cut a piece of material with a mitre saw and need to use the saw's angle gauge to make the cut) Thank you.
Q. Prove that α′(s) and α′′(s) are orthogonal.