1) Consider the curve r(t)= (5 sin 4 t, 5 cos 4 r, 3 t), answer the following Sketch/describe what this curve looks like and find its speed at any time r. Find the arc-length of one a. cycle of this curve (i.e., one period of the sin/cos; it isn't actually a closed curve, of course) and then re- parametrize this curve by arc-length. b. Find the unit tangent, the unit normal, and the unit binormal vectors for this curve at the point (4, 0, 0). Find the curvature at the same point. c. Find the tangential and normal components of acceleration at the point (4, 0, 0).

1) Consider the curve r(t)= (5 sin 4 t, 5 cos 4 r, 3 t), answer the following Sketch/describe what this curve looks like and find its speed at any time r. Find the arc-length of one a. cycle of this curve (i.e., one period of the sin/cos; it isn't actually a closed curve, of course) and then re- parametrize this curve by arc-length. b. Find the unit tangent, the unit normal, and the unit binormal vectors for this curve at the point (4, 0, 0). Find the curvature at the same point. c. Find the tangential and normal components of acceleration at the point (4, 0, 0).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 60E

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