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Show that the curve x = 3 cos(t), y = 2 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 = 2 sin(t) cos(t), we have the following. dx -3 sin t dt dy -2 sin² t - cos² t dt At the point (0, 0), we know that cos(t) = 0 , which only occurs at odd v multiples of *. On the interval [0, 2x), this only occurs at the following values. (Enter your answers as a comma-separated list.) dx At the smallest of these values, dt dy and dt dy ,so dx dx At the largest of these values found to meet the condition in [0, 2x), dt dy and dt dy so dx

Show that the curve x = 3 cos(t), y = 2 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 = 2 sin(t) cos(t), we have the following. dx -3 sin t dt dy -2 sin² t - cos² t dt At the point (0, 0), we know that cos(t) = 0 , which only occurs at odd v multiples of *. On the interval [0, 2x), this only occurs at the following values. (Enter your answers as a comma-separated list.) dx At the smallest of these values, dt dy and dt dy ,so dx dx At the largest of these values found to meet the condition in [0, 2x), dt dy and dt dy so dx

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Show that the curve x = 3 cos(t), y = 2 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 = 2 sin(t) cos(t), we have the following. dx -3 sin t dt - cos? : dy -2 sin? t t dt At the point (0, 0), we know that cos(t) = On the interval [0, 27), this only occurs at the following values. (Enter your 2 which only occurs at odd multiples of answers as a comma-separated list.) dx At the smallest of these values, dt dy and dt dy SO dx dx At the largest of these values found to meet the condition in [0, 2x), dt dy and dt dy so dx II II
Transcribed Image Text:Show that the curve x = 3 cos(t), y = 2 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 = 2 sin(t) cos(t), we have the following. dx -3 sin t dt - cos? : dy -2 sin? t t dt At the point (0, 0), we know that cos(t) = On the interval [0, 27), this only occurs at the following values. (Enter your 2 which only occurs at odd multiples of answers as a comma-separated list.) dx At the smallest of these values, dt dy and dt dy SO dx dx At the largest of these values found to meet the condition in [0, 2x), dt dy and dt dy so dx II II
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