For the smooth curve r(t), find the parametric equations for the line that is tangent to r at the given parameter value to P (1) = (5 tan t) i - (3 sin t) + (4 cos? t) k. Ox= 10 +5t y=--4 z = -4+ 21 Ox= 5+ 10r 3/2 z = 2+41 Ox= 5+ 10t y = -- z = 4-4t O x = 5+ 10t y = -- , z = 2-41

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 34E
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For the smooth curve r(t), find the parametric equations for the line that is tangent to r
at the given parameter value to = 7
r (1) = (5 tan t) i- (3 sin t) j + (4 cos² t) k.
O x = 10 + 5t
y = --
z = -4 + 21
O x = 5+ 10r
3y2
3 2
y = -2
z = 2 + 41
O x = 5+ 10r
y = -} -
z = 4 - 4t
O x = 5+ 10t
3/2
y = - - 2,
z = 2 – 41
Transcribed Image Text:For the smooth curve r(t), find the parametric equations for the line that is tangent to r at the given parameter value to = 7 r (1) = (5 tan t) i- (3 sin t) j + (4 cos² t) k. O x = 10 + 5t y = -- z = -4 + 21 O x = 5+ 10r 3y2 3 2 y = -2 z = 2 + 41 O x = 5+ 10r y = -} - z = 4 - 4t O x = 5+ 10t 3/2 y = - - 2, z = 2 – 41
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