PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter 6, Problem 82RE
Solution

To find: Parametric equations for the given situation that model Sarah’s position as a function of time (in seconds) if she started from the point 0,90 . At starting point t=0 .

  x=40sinπ9t and y=50+40cosπ9t

Given information:

Lowest point of wheel is 10 ft above the ground and its radius is 40 ft. Wheel completes one revolution is 18 seconds. Sarah is start moving from point 0,90 at t=0 seconds.

Formula used:

  sinθ=perpendicularhypotenuse and cosθ=basehypotenuse

Calculation:

Assume an arbitrary point Px,y , which is Sarah’s location at an angle θ . Suppose the wheel is rotating in the anticlockwise direction.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 6, Problem 82RE

Determine the x -coordinate of point P using the sine function. Apply the trigonometric ratio sinθ=perpendicularhypotenuse .

  sinθ=x40x=40sinθ

Determine the y -coordinate of point P using the cosine function. Apply the trigonometric ratio cosθ=basehypotenuse .

  cosθ=y504040cosθ=y50y=50+40cosθ

The wheel complete one revolution or 2π distance in every 18 seconds. Represent θ as a function of time (in seconds).

  θ=2π18t=π9t

Substitute θ=π9t into x=40sinθ and y=50+40cosθ to get the parametric equations.

  x=40sinπ9t

  y=50+40cosπ9t

Therefore, the parametric equations are x=40sinπ9t and y=50+40cosπ9t .

Chapter 6 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - Prob. 10ECh. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - 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