University:
Whitman College
Course:
MATH-225 | Calculus III
Academic year:

2010
Views:

294

Pages:

1
Author:

Ryann Hinton

642 CHAPTER 10 PARAMETRIC EQUATIONS AND POLAR COORDINATES 25–27 U se the graphs of x � f �t� and y � t�t� to sketch the parametric curve x � f �t�, y � t�t�. Indicate with arrows the direction in which the curve is traced as t increases. 19–22 D escribe the motion of a particle with position �x, y� as t varies in the given interval. 19. x � 3 � 2 cos t, y � 1 � 2 sin t, ��2 � t � 3��2 20. x � 2 sin t, y � 4 � cos t, 21. x � 5 sin t, y � 2 cos t, x 25. 0 � t � 3��2 1 �� t � 5� 1 y � cos2 t, �2� � t � 2� 22. x � sin t, y � t�t�, where the range of f is �1, 4� and the range of t is �2 , 3�. W hat can you say about the curve? 26. y � t�t� in (a)– (d) with the parametric curves labeled I – IV. G ive reasons for your choices. I y y 1 1 1 1 y 1 1 t 27. x 2 t x 1 24. M atch the graphs of the parametric equations x � f �t� and x 2 t 1 t 1 t _1 23. Suppose a curve is given by the parametric equations x � f �t�, (a) y y 1 1 1 2 x 1 t t t (b) II x 2 y 2 28. M atch the parametric equations with the graphs labeled I-V I. y 2 1t 1t (c) G ive reasons for your choices. (D o not use a graphing device.) (a) x � t 4 � t � 1, y � t 2 (b) x � t 2 � 2t, y � st (c) x � sin 2t, y � sin�t � sin 2t� (d) x � cos 5t, y � sin 2t (e) x � t � sin 4t, y � t 2 � cos 3t sin 2t cos 2t (f ) x � , y� 4 � t2 4 � t2 2 x III x 2 y y 1 2 2 t I III y y 2 x 1 2 t II y x x x (d) IV x 2 y 2 t y 2 IV 2 V y VI y 2 t y x 2 x x x

Parametric Equations and Polar Coordinates

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