All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.
When , using trigonometry identity, we find
For since and for principal values of
We have that when , its is a maximum point.
Using GC, Area
At maximum point,
To find the exact coordinates, students need to be able to either identify the correct trigonometry identify, or draw the right angled triangle to find and carefully. As for the show part for the parametric integration, students need to start from the definition of area then proceed carefully, not forgetting to change the limits.