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Show that the curve x = 3 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and find their equations. (Enter your answers as a comma-separated list.) Since x = 3 cos (t) and y = 5 sin(t) cos(t), we have the following. dx

Show that the curve x = 3 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and find their equations. (Enter your answers as a comma-separated list.) Since x = 3 cos (t) and y = 5 sin(t) cos(t), we have the following. dx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show that the curve x = 3 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and find their equations. (Enter your answers as a comma-separated list.) Since x = 3 cos (t) and y = 5 sin(t) cos(t), we have the following. dx dt dy dt At the point (0, 0), we know that cos(t) = ---Select--- V as a comma-separated list.) At the smallest of these values, y = Graph the curve. O -6 At the largest of these values found to meet the condition in [0, 2π), = dx dt dy dx Thus, there are two tangents to the curve x = 3 cos(t), y = 5 sin(t) cos(t), and their equations are as follows. (Enter your answers as a comma-separated list.) -6 -4 -4 -2 y 4 dx dt 2 2 2 4 4 6 and 6 X X which only occurs at ---Select--- Vmultiples of . On the interval [0, 2), this only occurs at the following values. (Enter your answers 2 dy dt i dy - 6 dy dt and = SO y 41 2 $ op X -4 -2 2 4 -6 -4 -2 2 -4 -4 6 6 X Q
Transcribed Image Text:Show that the curve x = 3 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and find their equations. (Enter your answers as a comma-separated list.) Since x = 3 cos (t) and y = 5 sin(t) cos(t), we have the following. dx dt dy dt At the point (0, 0), we know that cos(t) = ---Select--- V as a comma-separated list.) At the smallest of these values, y = Graph the curve. O -6 At the largest of these values found to meet the condition in [0, 2π), = dx dt dy dx Thus, there are two tangents to the curve x = 3 cos(t), y = 5 sin(t) cos(t), and their equations are as follows. (Enter your answers as a comma-separated list.) -6 -4 -4 -2 y 4 dx dt 2 2 2 4 4 6 and 6 X X which only occurs at ---Select--- Vmultiples of . On the interval [0, 2), this only occurs at the following values. (Enter your answers 2 dy dt i dy - 6 dy dt and = SO y 41 2 $ op X -4 -2 2 4 -6 -4 -2 2 -4 -4 6 6 X Q
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