![\"\"](\"/userfiles/image/steps_images/step1.JPG\")
(a)
\The parametric equations are ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a6572a1442a8d61e58c0ea987aa7dc63.png\")
and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=01ad583cda1a0d089dd8e5e72944dac1.png\")
.
Find the rectangular equation.
\Consider ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=01ad583cda1a0d089dd8e5e72944dac1.png\")
.
Substitute ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a6572a1442a8d61e58c0ea987aa7dc63.png\")
in .
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=197e6c12f681426a6bd623af2ee4d286.png\")
The rectangular equation is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=197e6c12f681426a6bd623af2ee4d286.png\")
.
Graph:
\Graph the parametric equations and .
![\"\"](\"/userfiles/48-718-33a.gif\")
Observe the graph :
\The domain of the graph is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a884b3c3c4acc19dc1398473286275c3.png\")
.
The orientation is Up and curve is smooth and continuous.
\The range is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9de658e7fcac17bc1614c5528fce227c.png\")
.
![\"\"](\"/userfiles/image/steps_images/step2.JPG\")
(b)
\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=ae460edc0836e6bf4c5215655502bcd4.png\")
.
Graph:
\Graph the parametric equations ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=fbab0a888980bbfacaa82f4c69330561.png\")
and ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=ae460edc0836e6bf4c5215655502bcd4.png\")
.
![\"\"](\"/userfiles/48-718-33b.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 Oscillating and curve is discontinuous at ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9a55befbd8fd23b0687c6deb65dbf93a.png\")
.
The range is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=581b3e937c6579f60fe60d9e628fe151.png\")
.
![\"\"](\"/userfiles/image/steps_images/step3.JPG\")
(c)
\The parametric equations are ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=dcacb12faff2d16aa3d658250d43f92c.png\")
and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=882ef081b0848602350a18d74c6513e2.png\")
.
Graph:
\Graph the parametric equations ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=dcacb12faff2d16aa3d658250d43f92c.png\")
and ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=882ef081b0848602350a18d74c6513e2.png\")
.
![\"\"](\"/userfiles/48-718-33c.gif\")
Observe the graph :
\The domain of the graph is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4fc4d31624beb147d45337ec04346e9e.png\")
.
The orientation is Down and curve is smooth and continuous.
\The range is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4e31a544a7cfcac0bf7dbe8fc5a489bd.png\")
.
![\"\"](\"/userfiles/image/steps_images/step4.JPG\")
(d)
\The parametric equations are ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=38a24ac9c2dbb856ac26cbb45fbf7974.png\")
and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9f181a65631c665b13508f5c1e1c1808.png\")
.
Graph:
\Graph the parametric equations ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=38a24ac9c2dbb856ac26cbb45fbf7974.png\")
and ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9f181a65631c665b13508f5c1e1c1808.png\")
.
![\"\"](\"/userfiles/48-718-33d.gif\")
Observe the graph :
\The domain of the graph is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4fc4d31624beb147d45337ec04346e9e.png\")
.
The orientation is Up and curve is smooth and continuous.
\The range is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4e31a544a7cfcac0bf7dbe8fc5a489bd.png\")
.
Observe the set of graphs of parametric equations:
\The parametric equations from (a)-(d) are similar and their rectangular equation is .
They differ in orientation and some are domain restricted.
\![\"\"](\"/userfiles/image/steps_images/solution.JPG\")
The parametric equations from (a)-(d) are similar and their rectangular equation is .
They differ in orientation and some are domain restricted.
\(a)
\The domain of the graph is .
The orientation is Up and curve is smooth and continuous.
\The range is .
(b)
\The domain of the graph is .
The orientation is Oscillating and curve is discontinuous at .
The range is .
(c)
\The domain of the graph is .
The orientation is Down and curve is smooth and continuous.
\The range is .
(d)
\The domain of the graph is .
The orientation is Up and curve is smooth and continuous.
\The range is .