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EXAMPLE 2 What curve is represented by the following parametric equations? x = 2 cos(t) y = 2 sin(t) osts 2n SOLUTION If we plot points, it appears that the curve is a circle. We can confirm this impression by eliminating t. Observe that x² + y? = 4 cos²(t) + Thus the point (x, y) moves on the circle x? + y2 = Notice that in this example the parameter t can be interpreted as the angle (in radians) shown in the figure. As t increases from 0 to 27, the point (x, y) = (2 cos(t), 2 sin(t)) moves once around the circle in the ---Select-- v direction starting at the point (x, y) =

EXAMPLE 2 What curve is represented by the following parametric equations? x = 2 cos(t) y = 2 sin(t) osts 2n SOLUTION If we plot points, it appears that the curve is a circle. We can confirm this impression by eliminating t. Observe that x² + y? = 4 cos²(t) + Thus the point (x, y) moves on the circle x? + y2 = Notice that in this example the parameter t can be interpreted as the angle (in radians) shown in the figure. As t increases from 0 to 27, the point (x, y) = (2 cos(t), 2 sin(t)) moves once around the circle in the ---Select-- v direction starting at the point (x, y) =

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.CT: Chapter Test
Problem 7CT
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EXAMPLE 2 What curve is represented by the following parametric equations? x = 2 cos(t) y = 2 sin(t) osts 2n SOLUTION If we plot points, it appears that the curve is a circle. We can confirm this impression by eliminating t. Observe that x² + y? = 4 cos²(t) + Thus the point (x, y) moves on the circle x? + y2 = Notice that in this example the parameter t can be interpreted as the angle (in radians) shown in the figure. As t increases from 0 to 27, the point (x, y) = (2 cos(t), 2 sin(t)) moves once around the circle in the ---Select-- v direction starting at the point (x, y) =
Transcribed Image Text:EXAMPLE 2 What curve is represented by the following parametric equations? x = 2 cos(t) y = 2 sin(t) osts 2n SOLUTION If we plot points, it appears that the curve is a circle. We can confirm this impression by eliminating t. Observe that x² + y? = 4 cos²(t) + Thus the point (x, y) moves on the circle x? + y2 = Notice that in this example the parameter t can be interpreted as the angle (in radians) shown in the figure. As t increases from 0 to 27, the point (x, y) = (2 cos(t), 2 sin(t)) moves once around the circle in the ---Select-- v direction starting at the point (x, y) =
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