Let C be the curve parameterized by c(t) = (sin(t) + 2sin(2t), cos(t) - 2 cos(2t)),...

  

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Let C be the curve parameterized by c(t) = (sin(t) + 2sin(2t), cos(t) - 2 cos(2t)), t [0,2]. (a) Draw a sketch of C in a well-labeled coordinate plane. You may find it helpful to use an online parametric curve sketcher, knot you will draw is a famous knot called the trefoil knot. The (b) Argue based on your intuition whether or not C is unknotted, i.e. whether or not it can be continuously deformed into a circle without self-intersection. (c) Set up the integral to compute the are length of the trefoil knot. 700 x 24 Let C be the curve parameterized by c(t) = (sin(t) + 2sin(2t), cos(t) - 2 cos(2t)), t [0,2]. (a) Draw a sketch of C in a well-labeled coordinate plane. You may find it helpful to use an online parametric curve sketcher, knot you will draw is a famous knot called the trefoil knot. The (b) Argue based on your intuition whether or not C is unknotted, i.e. whether or not it can be continuously deformed into a circle without self-intersection. (c) Set up the integral to compute the are length of the trefoil knot. 700 x 24

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A beautiful problem a Sketch of C Ill use a parametric curve sketcher to draw the trefoil knot Heres ... View the full answer