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Let C be a curve that is defined by x = 4 sint and y = cos t, t e [0, 27]. Determine (a) the time intervals on which the curve is (i) increasing, and (ii) decreasing;

Let C be a curve that is defined by x = 4 sint and y = cos t, t e [0, 27]. Determine (a) the time intervals on which the curve is (i) increasing, and (ii) decreasing;

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 62E
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Let C be a curve that is defined by x = 4 sin t and y = cos t, t e [0, 27). Determine (a) the time intervals on which the curve is (i) increasing, and (ii) decreasing; (b) the time intervals on which the graph is (i) concave upward, and (ii) concave downward; (c) (i) the cartesian points (x, y) of the curve where horizontal tangent lines exist, and (ii) the cartesian points (x, y) of the curve where vertical tangent lines exist; 11T (d) the equation of the line tangent to the curve at the point where (i) t = , and (ii) t = CS Scanned with CamScarner
Transcribed Image Text:Let C be a curve that is defined by x = 4 sin t and y = cos t, t e [0, 27). Determine (a) the time intervals on which the curve is (i) increasing, and (ii) decreasing; (b) the time intervals on which the graph is (i) concave upward, and (ii) concave downward; (c) (i) the cartesian points (x, y) of the curve where horizontal tangent lines exist, and (ii) the cartesian points (x, y) of the curve where vertical tangent lines exist; 11T (d) the equation of the line tangent to the curve at the point where (i) t = , and (ii) t = CS Scanned with CamScarner
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