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.
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