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What minimum parameter domain is required to draw the entire circle? Ost< How many times is the circle traced out for 0sts 4n? Click the Animate button and observe the relationship between the parametric graph and the individual graphs. Can you see howa combination of sine and cosine waves in the individual functions results in a circle? (b) Change the equations to x= 3 cos(21). y = 3 sin(21). Compare the parametric curve to that of part (a). O The curve is the same as part (a), and is traced the same. O The curve is the same as part (a), but has half the radius. O The curve is the same as part (a), but it is traced twice as fast. O The curve is the same as part (a), but has twice the radius. O The curve is different from part (a). How many times is the circle traced out for 0sts 4n? (c) Change the equations to x = 3 cos(-21). y = 3 sin(-21). Compare to the graph in part (b). Is the circle the same? is it traced out in the same manner? O The curve remains the same, and is traced out in the same manner. O The curve remains the same, but in part (b) the circle is traced counter clockwise as t increases and in this case the circle is traced clockwise. O The curve remains the same, but in part (b) the circle is traced clockwise as t increases and in this case the circle is traced counter clockwise. (d) Write parametric equations for a circle of radius 2, centered at the origin that is traced out once in the clockwise direction for 0sts 4. Use the module to verity your result. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (xCO. y0) = (

What minimum parameter domain is required to draw the entire circle? Ost< How many times is the circle traced out for 0sts 4n? Click the Animate button and observe the relationship between the parametric graph and the individual graphs. Can you see howa combination of sine and cosine waves in the individual functions results in a circle? (b) Change the equations to x= 3 cos(21). y = 3 sin(21). Compare the parametric curve to that of part (a). O The curve is the same as part (a), and is traced the same. O The curve is the same as part (a), but has half the radius. O The curve is the same as part (a), but it is traced twice as fast. O The curve is the same as part (a), but has twice the radius. O The curve is different from part (a). How many times is the circle traced out for 0sts 4n? (c) Change the equations to x = 3 cos(-21). y = 3 sin(-21). Compare to the graph in part (b). Is the circle the same? is it traced out in the same manner? O The curve remains the same, and is traced out in the same manner. O The curve remains the same, but in part (b) the circle is traced counter clockwise as t increases and in this case the circle is traced clockwise. O The curve remains the same, but in part (b) the circle is traced clockwise as t increases and in this case the circle is traced counter clockwise. (d) Write parametric equations for a circle of radius 2, centered at the origin that is traced out once in the clockwise direction for 0sts 4. Use the module to verity your result. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (xCO. y0) = (

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A-D Parametric curves

 

 

Select the first set of parametric equations, x= a cos(bt), y = c sin(at). (a) Set the equations to x= 3 cos(t), y = 3 sin(t) using the sliders for a, b, c, and d. Describe the parametric curve.
Transcribed Image Text:Select the first set of parametric equations, x= a cos(bt), y = c sin(at). (a) Set the equations to x= 3 cos(t), y = 3 sin(t) using the sliders for a, b, c, and d. Describe the parametric curve.
What minimum parameter domain is required to draw the entire circle? Ost< How many times is the circle traced out for 0sts 4n? Click the Animate button and observe the relationship between the parametric graph and the individual graphs. Can you see how a combination of sine and cosine waves in the individual functions results in a circle? (b) Change the equations to x = 3 cos(2t), y = 3 sin(2f). Compare the parametric curve to that of part (a). O The curve is the same as part (a), and is traced the same. O The curve is the same as part (a), but has half the radius. O The curve is the same as part (a), but it is traced twice as fast. O The curve is the same as part (a), but has twice the radius. O The curve is different from part (a). How many times is the circle traced out for 0sts 4n? (c) Change the equations to x = 3 cos(-2t), y = 3 sin(-2t). Compare to the graph in part (b). Is the circle the same? Is it traced out in the same manner? O The curve remains the same, and is traced out in the same manner. O The curve remains the same, but in part (b) the circle is traced counter clockwise as t increases and in this case the circle is traced clockwise. O The curve remains the same, but in part (b) the circle is traced clockwise as t increases and in this case the circle is traced counter clockwise. (d) Write parametric equations for a circle of radius 2, centered at the origin that is traced out once in the clockwise direction for 0sts 47. Use the module to verify your result. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (x(1), y(t) =
Transcribed Image Text:What minimum parameter domain is required to draw the entire circle? Ost< How many times is the circle traced out for 0sts 4n? Click the Animate button and observe the relationship between the parametric graph and the individual graphs. Can you see how a combination of sine and cosine waves in the individual functions results in a circle? (b) Change the equations to x = 3 cos(2t), y = 3 sin(2f). Compare the parametric curve to that of part (a). O The curve is the same as part (a), and is traced the same. O The curve is the same as part (a), but has half the radius. O The curve is the same as part (a), but it is traced twice as fast. O The curve is the same as part (a), but has twice the radius. O The curve is different from part (a). How many times is the circle traced out for 0sts 4n? (c) Change the equations to x = 3 cos(-2t), y = 3 sin(-2t). Compare to the graph in part (b). Is the circle the same? Is it traced out in the same manner? O The curve remains the same, and is traced out in the same manner. O The curve remains the same, but in part (b) the circle is traced counter clockwise as t increases and in this case the circle is traced clockwise. O The curve remains the same, but in part (b) the circle is traced clockwise as t increases and in this case the circle is traced counter clockwise. (d) Write parametric equations for a circle of radius 2, centered at the origin that is traced out once in the clockwise direction for 0sts 47. Use the module to verify your result. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (x(1), y(t) =
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