![\"\"](\"/userfiles/image/steps_images/step1.JPG\")
(a)
\The parametric equations are ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=fbab0a888980bbfacaa82f4c69330561.png\")
and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=0a5a9ef8c3d181a069d629dfa8fee6e2.png\")
.
Find the rectangular equation.
\Consider ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=fbab0a888980bbfacaa82f4c69330561.png\")
.
Squaring on each side.
\![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=70318e0ff3f6d7bce7ed8e764863d3f6.png\")
.
Consider ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=38fb8efcbb55f7527a354fbef787078b.png\")
.
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=097ef56a11c6393cf2feb30f67b70bb6.png\")
Trigonometric identity: ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=c010bb9f2bd1c342d7c90990a1511122.png\")
.
Substitute ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=70318e0ff3f6d7bce7ed8e764863d3f6.png\")
and ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=097ef56a11c6393cf2feb30f67b70bb6.png\")
.
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=01699a75f878a2e4b15534c74dfdbcdc.png\")
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4c161da09002705acff351e608152069.png\")
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=3df57c90cf572186c4df6052df9e401e.png\")
The rectangular equation is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=3df57c90cf572186c4df6052df9e401e.png\")
.
Graph:
\Graph the parametric equations and .
![\"\"](\"/userfiles/48-718-35a(1).gif\")
.
Observe the graph:
\The domain of the graph is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=0b3049f09d664908a6733a73c6f0289a.png\")
.
The orientation is from right to left and curve is smooth and continuous on the interval.
\The range is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=51141e31a6271e0918080e8c62ecc431.png\")
.
![\"\"](\"/userfiles/image/steps_images/step2.JPG\")
(b)
\The parametric equations are ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=5431081f04046d158b102e1a396835cf.png\")
and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=2a1c4abf6c104b0a2d06939e85329a5b.png\")
.
Graph:
\Graph the parametric equations ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=5431081f04046d158b102e1a396835cf.png\")
and ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=2a1c4abf6c104b0a2d06939e85329a5b.png\")
.
![\"\"](\"/userfiles/48-718-35b.gif\")
.
Observe the graph:
\The domain of the graph is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=0b3049f09d664908a6733a73c6f0289a.png\")
.
The orientation is from right to left and curve is smooth and continuous on the interval.
\The range is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=51141e31a6271e0918080e8c62ecc431.png\")
.
Observe the set of graphs of parametric equations:
\The parametric equations from (a)-(b) are similar and their rectangular equation is .
The curves are identical in the interval ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=360d389828dc6bc266e4fe12b603d3c3.png\")
and it orientation is from right to left.
![\"\"](\"/userfiles/image/steps_images/solution.JPG\")
The parametric equations from (a)-(b) are similar and their rectangular equation is .
The curves are identical in the interval ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=360d389828dc6bc266e4fe12b603d3c3.png\")
and it orientation is from right to left.
(a)
\The domain of the graph is .
The orientation is from right to left and curve is smooth and continuous on the interval.
\The range is .
(b)
\The domain of the graph is .
The orientation is from right to left and curve is smooth and continuous on the interval.
\The range is .