The curve in the ry-plane given by the para- metric equations x = cos t, y...

 

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The curve in the ry-plane given by the para- metric equations x = cos t, y = sin 2t, 0 <t < 2n, called a Lissajous figure, is symmetric about both axes. (a) Fill in the table below, then sketch the curve. t T/4 T/3 T/2 (b) Find an equation for the tangent line to the curve at the point cor- responding tot = 1/6. You may leave your answer in point-slope form. (c) Set up an integral that gives the exact length of the curve. Do not evaluate the integral. You may use symmetry. The curve in the ry-plane given by the para- metric equations x = cos t, y = sin 2t, 0 <t < 2n, called a Lissajous figure, is symmetric about both axes. (a) Fill in the table below, then sketch the curve. t T/4 T/3 T/2 (b) Find an equation for the tangent line to the curve at the point cor- responding tot = 1/6. You may leave your answer in point-slope form. (c) Set up an integral that gives the exact length of the curve. Do not evaluate the integral. You may use symmetry.

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