8/9/2019 HMA Section 6.4 Notes

1/49

Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1

Homework, Page 530

Match the parametric equations with their graph. Identify the

viewing window that seems to have been used.1.

b. The window appears to be

3 34cos , 2sinx t y t= =

[ ] [ ], by !,!

8/9/2019 HMA Section 6.4 Notes

2/49

Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 2

Homework, Page 530

"a# $omp%ete the tab%e for the parametric equations and "b# p%ot the

corresponding points!.

32, 1x t yt

= + = +

t &2 &1 ' 1 2

x ' 1 2 3 4y &'.! &2 (nd. 4 2.!

4 3 2 1 1 2 3 4

2

1

1

2

3

4

8/9/2019 HMA Section 6.4 Notes

3/49

Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 3

Homework, Page 530

)raph the parametric equationsx* 3 & t2,y* 2tin the specified

parameter interva%. (se the standard viewing window.+. 3 3x

109 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

9

8

76

5

4

3

2

1

1

23

4

5

6

7

8

9

8/9/2019 HMA Section 6.4 Notes

4/49

Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 4

Homework, Page 530

%iminate the parameter and identify the graph of the parametric

curve.13. 2 3, + 4 ,3 !x t y t t= =

32 3 2 3

2

xx t t x t

+= = + =

3

+ 4 + 2 2 32

x

y x y x

+

= = = + ( ) ( )3 3 3, ! 1' 3 -x x= = = =

( ) ( ) ( ) ( )3 2 3 3 3 - 2 - 3 11y y= + = = + =

( ) ( )/ %ine segment from 3, 3 to -, 11

8/9/2019 HMA Section 6.4 Notes

5/49

8/9/2019 HMA Section 6.4 Notes

6/49

Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 6

Homework, Page 530

%iminate the parameter and identify the graph of the parametric

curve.21.

23, , ! !!

x t y tt

= =

( )

2 23,

3 ! 2t x y y

x x= + = =

+

( ) ( )! 3 0, ! 3 2x x= = = =

[ ]The graph is of a reciproca% function on interva% 0,2

8/9/2019 HMA Section 6.4 Notes

7/49Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 7

Homework, Page 530

%iminate the parameter and identify the graph of the parametric

curve.2!.

32sin , 2cos ,'2

x t y t t = =

2 2 2 24sin , 4cosx t y t= =

2 1 1 2

2

1

1

2

( )2 2 2 24 sin cosx y t t + = +2 2

4x y+ =

The graph is a circ%e of radius 2 in quadrants I, III, and I.

8/9/2019 HMA Section 6.4 Notes

8/49Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 8

Homework, Page 530

ind a parameteriation for the curve.

2+. The %ine segment with endpoints "3, 4# and ", &3#.

( ) ( )3,4 , , 3

et 3 3x t= + ( ) ( ) ( ) ( )' 3 ' 3 3, 1 3 1 3 x x = + = = + =

( )( )-

4 3 3 3 4 - 4 -3

y t y t y t = + = =

3 3, 4 - ,' 1x t y t t= + =

3 4 -

3 3m

= =

( )

-4 3

3y x =

8/9/2019 HMA Section 6.4 Notes

9/49Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 9

Homework, Page 530

5efer to the graph of the parametric equations

given be%ow. ind the va%ues ofthe parameter tthat produce the graph in the indicated quadrant.

33. 6uadrant I

2 , '.!, 3 3x t y t t= =

2 , '.!, 3 3x t y t t= =

' 2 2x t> < > '.! 2t