lab11_w13 - Math 118 Lab 11 Winter 2013 Parametric equations parametric curves polar coordinates polar equations polar curves Not to be handed in for

# lab11_w13 - Math 118 Lab 11 Winter 2013 Parametric...

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Math 118 - Lab 11 - Winter 2013. Parametric equations, parametric curves, polar coordinates, polar equations, polar curves. Not to be handed in for marking. Parametric equations and curves. 1. Sketch the curve of the parametric equations braceleftBigg x = sec 2 t - 1 y = tan t for - π/ 2 < t < π/ 2 2. Sketch the curve of the parametric equations braceleftBigg x = t 2 + t y = t 2 - t for -∞ < t < . (It may help to determine the x and y intercepts as well as determine the derivatives at those points. ) 3. The curve of the parametric equations braceleftBigg x = sin t y = sin (2 t ) for 0 < t < 4 π is called the Lissajous curve . (a) Determine all the x and y intercepts. (b) Use derivatives to determine the points where the curve has horizontal tangent lines and vertical tangent lines. (c) Sketch the graph. Polar equations and polar curves. 4. Convert the following rectangular ( x, y ) points to polar form ( r, θ ), or vice versa. Use r 0 and 0 θ 2 π for the polar form points so that the polar forms will be unique