Difference between revisions of "009C Sample Final 3, Problem 7"

Revision as of 17:59, 4 March 2017

A curve is given in polar coordinates by

r=1+\cos ^{2}(2\theta )

(a) Show that the point with Cartesian coordinates $(x,y)={\bigg (}{\frac {\sqrt {2}}{2}},{\frac {\sqrt {2}}{2}}{\bigg )}$ belongs to the curve.

(b) Sketch the curve.

(c) In Cartesian coordinates, find the equation of the tangent line at ${\bigg (}{\frac {\sqrt {2}}{2}},{\frac {\sqrt {2}}{2}}{\bigg )}.$

Solution:

(a)

Step 2:

(b)

Step 2:

(c)

Step 2:

@@ Line 1: / Line 1: @@
 <span class="exam">A curve is given in polar coordinates by
-::::::<math>r=1+\cos^2(2\theta)</math>
+::<math>r=1+\cos^2(2\theta)</math>
-::<span class="exam">a) Show that the point with Cartesian coordinates <math>(x,y)=\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg)</math> belongs to the curve.
+<span class="exam">(a) Show that the point with Cartesian coordinates &nbsp;<math>(x,y)=\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg)</math>&nbsp; belongs to the curve.
-::<span class="exam">b) Sketch the curve.
+<span class="exam">(b) Sketch the curve.
-::<span class="exam">c) In Cartesian coordinates, find the equation of the tangent line at <math>\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg).</math>
+<span class="exam">(c) In Cartesian coordinates, find the equation of the tangent line at &nbsp;<math>\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg).</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 22: / Line 22: @@
 |
 |}
 '''Solution:'''
@@ Line 64: / Line 65: @@
 |
 |}
+'''(c)'''
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+!Step 1: &nbsp;
+|-
+|
+|-
+|
+|-
+|
+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+!Step 2: &nbsp;
+|-
+|
+|-
+|
+|}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 71: / Line 93: @@
 |-
 |&nbsp;&nbsp; '''(b)'''
+|-
+|&nbsp;&nbsp; '''(c)'''
 |}
 [[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]