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Find the area of the region bounded by the graph of \(r=sec\theta,\) the graph of \(r = \csc \theta,\) the \(x\)-axis, and the \(y\)-axis.

 Aug 24, 2019
 #1
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We can transform these polar equations to cartesian equations as follows :

 

r  = sec θ                                                           r = csc θ

r = r / x   divide both sides by r                          r =  r/y        divide both sides by r

1 = 1/x     multiply both sides by x                     1  = 1/y      multiply both sides by y

x  =  1                                                                  y = 1

 

So  .....this area is a square of side 1  bounded by  the line x = 1, y =1, the x axis and the y axis

 

And the area of the region  is just  side^2  =  1^2    =   1

 

See the graph of the region here : https://www.desmos.com/calculator/bwbzmhrslp

 

cool cool cool

 Aug 24, 2019

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