Parametric Curves Calculus III Lab LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnRitGOkY9 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

The syntax for plotting parametric equations is 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 where f and g are the specific parametric functions for x and y in terms of t. For the parametric equation of the parabola of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUkobWZlbmNlZEdGJDYkLUYjNiUtRlc2Ji1GIzYrRistRiM2Ji1JJW1zdXBHRiQ2JS1GLDYlUSJ0RidGNkY5LUkjbW5HRiQ2JFEiMkYnRkAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY9Ni1RKCZtaW51cztGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjIyMjIyMmVtRicvRlVGXHAtRmJvNiRRIjRGJ0ZARkAtRj02LVEiLEYnRkBGQi9GRkY4RkdGSUZLRk1GT0ZRL0ZVUSwwLjMzMzMzMzNlbUYnLUkmbWZyYWNHRiQ2KC1GIzYlRl5vLyUrZXhlY3V0YWJsZUdGREZALUYjNiVGYW9GXHFGQC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZXEvJSliZXZlbGxlZEdGREZhcC1GIzYoRl5vLUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGYHItRiM2KEYrLUYjNiYtRj02LVEqJnVtaW51czA7RidGQEZCRkVGR0ZJRktGTUZPRltwRl1wRmFvRlxxRkAtRj02LVEjLi5GJ0ZARkJGRUZHRklGS0ZNRk9GW3BGVC1GYm82JFEiM0YnRkBGXHFGQEYrRlxxRkBGK0ZccUZARkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGXHFGQEZARlxxRkBGK0ZccUZARitGXHFGQA== 2. You can right click on the graph above and choose various options to enhance the plot Note that we don't know the positive orientation of the curve -- to see how it is generated over the minimum to maximum range of t, we can animate the plot with animatecurve (note all that is changed is the word plot is changed to animatecurve). To see the animation execute the command, then select the plot output with the mouse and click on the play button. 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

The plots below are plots of the curve represented by the parametric equation of a circle: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, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUkobWZlbmNlZEdGJDYkLUYjNiUtRlc2Ji1GIzYrRistRiM2Jy1GLDYlUSRjb3NGJy9GN0ZERkBGPC1GVzYkLUYjNiUtRiw2JVEidEYnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQEZARmZvRkAtRj02LVEiLEYnRkBGQi9GRkY4RkdGSUZLRk1GT0ZRL0ZVUSwwLjMzMzMzMzNlbUYnLUYjNictRiw2JVEkc2luRidGXm9GQEY8Rl9vRmZvRkBGaG8tRiM2KEZjby1GPTYtUSI9RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjI3Nzc3NzhlbUYnL0ZVRmlwLUYjNigtSSNtbkdGJDYkUSIwRidGQC1GPTYtUSMuLkYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yMjIyMjIyZW1GJ0ZULUYjNiYtRl5xNiRRIjJGJ0ZALUY9Ni1RMSZJbnZpc2libGVUaW1lcztGJ0ZARkJGRUZHRklGS0ZNRk9GUUZULUYsNiVRJyYjOTYwO0YnRl5vRkBGQEYrRmZvRkBGK0Zmb0ZARitGZm9GQEZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmZvRkBGQEZmb0ZARitGZm9GQEYrRmZvRkA= 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 Plot the parametric equations for the circle for exercise 20, page 631: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Plot the parametric equations for the line segment in exercise 33: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Plot the curve in exercise 42, page 631 plot on the range 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 JSFH

Enter the commands (plot first, then animatecurve) to show the plot (and then orientation) of the "Lissajous curve" given by the parametric equations 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. Note for the animatecurve is too "rough" when you first try it. Add the options numpoints = 100, frames = 100 to the animate curve command (after scaling = constrained, ) to get a more refined animation. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUkobWZlbmNlZEdGJDYkLUYjNigtRlc2Ji1GIzYrRistRiM2Jy1GLDYlUSRjb3NGJy9GN0ZERkBGPC1GVzYkLUYjNidGKy1GIzYmLUkjbW5HRiQ2JFEiM0YnRkAtRj02LVExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlQtRiw2JVEidEYnRjZGOUZARisvJStleGVjdXRhYmxlR0ZERkBGQEZfcEZALUY9Ni1RIixGJ0ZARkIvRkZGOEZHRklGS0ZNRk9GUS9GVVEsMC4zMzMzMzMzZW1GJy1GIzYnLUYsNiVRJHNpbkYnRl5vRkBGPC1GVzYkLUYjNidGKy1GIzYmLUZmbzYkUSI1RidGQEZpb0ZccEZARitGX3BGQEZARl9wRkBGYXAtRiM2KEZccC1GPTYtUSI9RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjI3Nzc3NzhlbUYnL0ZVRltyLUYjNigtRmZvNiRRIjBGJ0ZALUY9Ni1RIy4uRidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjIyMjIyMjJlbUYnRlQtRiM2Ji1GZm82JFEiMkYnRkBGaW8tRiw2JVEnJiM5NjA7RidGXm9GQEZARitGX3BGQEYrRl9wRkBGK0ZfcEZARkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGYXAtRiM2Jy1GLDYlUShzY2FsaW5nRidGNkY5RmdxLUYsNiVRLGNvbnN0cmFpbmVkRidGNkY5Rl9wRkBGK0ZfcEZARkBGX3BGQEYrRl9wRkBGK0ZfcEZA 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

Hypocycloid ("under the wheel") as the curve traced by a fixed point on a circle of radius B (smaller) as it rotates around the inside of a circle of radius A (larger). The parametric equations for a hypocycloid are given by: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYjNihGKy1GIzYnLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEiQUYnRjRGNy1GOzYtUSgmbWludXM7RidGPkZARkNGRUZHRklGS0ZNL0ZQUSwwLjIyMjIyMjJlbUYnL0ZTRl5vLUYsNiVRIkJGJ0Y0RjdGPkY+LUY7Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRJjAuMGVtRicvRlNGZ28tRiM2Ji1GLDYlUSRzaW5GJy9GNUZCRj4tRjs2LVEwJkFwcGx5RnVuY3Rpb247RidGPkZARkNGRUZHRklGS0ZNRmZvRmhvLUZZNiQtRiM2JC1GLDYlUSJ0RidGNEY3Rj5GPkY+RitGPkZqbi1GIzYnRmBvRmNvLUYjNiZGW3BGX3AtRlk2JC1GIzYkLUkmbWZyYWNHRiQ2KC1GIzYmRlhGY29GZnBGPi1GIzYkRmBvRj4vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl1yLyUpYmV2ZWxsZWRHRkJGPkY+Rj5GK0Y+RitGPkYrRj5GK0Y+ The term epicycloid ( "upon the wheel") refers to the curve traced by a fixed point on a circle of radius B (smaller) as it rotates around the inside of a circle of radius A (larger), and is given by the parametric equations: 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 Command to plot a hypocycloid - LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEiOEYnRjktRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0Y9Rjk=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 3. Command to plot an epicycloid -- 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 JSFH