A Cartesian and apolar graph of31=2- 5 cos (40)are given. Identifythe points on thepolar graph thatcorrespond to thepoints shown onthe Cartesiangraph.JAMOO12πⒸON-8LOto8 Which point on the polar graph corresponds to point A on the Cartesian graph?pointWhich point on the polar graph corresponds to point B on the Cartesian graph?pointWhich point on the polar graph corresponds to point C on the Cartesian graph?point

From the given polar curve of Given that a polar graph is periodic with a period,The point A is…

Answered: A Cartesian and a polar graph of 3 1=2…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

A Cartesian and a
polar graph of
3
1=2
- 5 cos (40)
are given. Identify
the points on the
polar graph that
correspond to the
points shown on
the Cartesian
graph.
JAM
O
O
12π
ⒸON
-8
LO
to
8

Which point on the polar graph corresponds to point A on the Cartesian graph?
point
Which point on the polar graph corresponds to point B on the Cartesian graph?
point
Which point on the polar graph corresponds to point C on the Cartesian graph?
point

Expert Solution

Step 1: Description of given data

From the given polar curve of $r equals 3 over 2 minus 5 cos left parenthesis 4 theta right parenthesis$

Given that a polar graph is periodic with a period, $theta equals pi over 2$

The point A is obtained by substituting the maximum value of r as follows:

$r equals 3 over 2 minus 5 cos left parenthesis 4 theta right parenthesis equals 3 over 2 minus 5 left parenthesis negative 1 right parenthesis equals 1.5 plus 5 equals 6.5$

i.e.,

$cos left parenthesis 4 theta right parenthesis equals negative 1 4 theta equals 3 pi theta equals fraction numerator 3 pi over denominator 4 end fraction$

$therefore space theta subscript A equals fraction numerator 3 pi over denominator 4 end fraction$ , $r subscript A equals 6.5$

Similarly for point B:

The point B is obtained by substituting the minimum value of r as follows:

$r equals 3 over 2 minus 5 cos left parenthesis 4 theta right parenthesis equals 3 over 2 minus 5 left parenthesis 1 right parenthesis equals 1.5 minus 5 equals negative 3.5$

i.e.,

$cos left parenthesis 4 theta right parenthesis equals 1 4 theta equals 6 pi theta equals fraction numerator 3 pi over denominator 2 end fraction$

$therefore space theta subscript B equals fraction numerator 3 pi over denominator 2 end fraction comma space r subscript B equals negative 3.5$

Now point C is obtained by substituting $r equals 0$

$3 over 2 minus 5 cos left parenthesis 4 theta right parenthesis equals 0 5 cos left parenthesis 4 theta right parenthesis equals 3 over 2 cos left parenthesis 4 theta right parenthesis equals 3 over 10 theta equals 1 fourth cos to the power of negative 1 end exponent open parentheses 3 over 10 close parentheses$