Find r, T, N, and B at the given value of t. Then find the equations for the osculating, normal, and rectifying planes at that value of t. π r(t) = (cos t)i + (sin t)j-2k, t= -

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 64E
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Find r, T, N, and B at the given value of t. Then find the equations for the osculating, normal, and rectifying planes at that value of t.
π
r(t) = (cos t)i + (sin t)j-2k, t=
I
i+
+0₁
k
(Type exact answers, using radicals as needed.)
¹(³)=0¹0¹0*
1+
(Type exact answers, using radicals as needed.)
+
N
(1) = 0·0.
k
(Type exact answers, using radicals as needed.)
B
(1) = 0·0¹0
i+D. k
(Type exact answers, using radicals as needed.)
π
The osculating plane at t = = is
4
(Type an equation.)
Л
The normal plane at t = = is
4
(Type an equation.)
π
The rectifying plane at t = = is
(Type an equation.)
Transcribed Image Text:Find r, T, N, and B at the given value of t. Then find the equations for the osculating, normal, and rectifying planes at that value of t. π r(t) = (cos t)i + (sin t)j-2k, t= I i+ +0₁ k (Type exact answers, using radicals as needed.) ¹(³)=0¹0¹0* 1+ (Type exact answers, using radicals as needed.) + N (1) = 0·0. k (Type exact answers, using radicals as needed.) B (1) = 0·0¹0 i+D. k (Type exact answers, using radicals as needed.) π The osculating plane at t = = is 4 (Type an equation.) Л The normal plane at t = = is 4 (Type an equation.) π The rectifying plane at t = = is (Type an equation.)
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