Difference between revisions of "009C Sample Final 3, Problem 7"
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::<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 <math style="vertical-align: -15px">(x,y)=\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg)</math> 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 <math style="vertical-align: -15px">\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg).</math> |
{| class="mw-collapsible mw-collapsed" style = "text-align:left;" | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||
Revision as of 18:21, 4 March 2017
A curve is given in polar coordinates by
(a) Show that the point with Cartesian coordinates belongs to the curve.
(b) Sketch the curve.
(c) In Cartesian coordinates, find the equation of the tangent line at
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Solution:
(a)
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(b)
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(c)
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| (a) |
| (b) |
| (c) |