Explanation Given information: The parametric equations for the motion of a particle in the x y -plane is given as follows: x = ( 1 / 2 ) tan t (1) y = ( 1 / 2 ) sec t (2) The parameter intervals are given as follows: − π / 2 < t < π / 2 Calculation: Take square on both sides of Equation (1) as follows: x 2 = ( 1 2 tan t ) 2 = 1 4 tan 2 t Rearrange the expression as follows: 4 x 2 = tan 2 t Take square on both sides of Equation (2) as follows: y 2 = ( 1 2 sec t ) 2 = 1 4 sec 2 t Rearrange the expression as follows: 4 y 2 = sec 2 t Write the expression for the trigonometric identity for tan 2 t as follows: tan 2 t + 1 = sec 2 t (3) Substitute

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Chapter 11, Problem 3PE

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Find the Cartesian equation for the parametric equations x=(1/2)tant, y=(1/2)sect; −π/2<t<π/2 and draw its graph in xy plane.

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Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...

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Find the Cartesian equation for the parametric equations x = ( 1 / 2 ) tan t , y = ( 1 / 2 ) sec t ; − π / 2 &lt; t &lt; π / 2 and draw its graph in xy plane.

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Find the Cartesian equation for the parametric equations x=(1/2)tant, y=(1/2)sect; −π/2<t<π/2 and draw its graph in xy plane.

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Find the Cartesian equation for the parametric equations x = ( 1 / 2 ) tan t , y = ( 1 / 2 ) sec t ; − π / 2 < t < π / 2 and draw its graph in xy plane.