Polar coordinates of a point are given. Find therectangular coordinates of the point. (-3,-135^(circ))

Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).

How do I integrate ${\displaystyle \sin \theta +\sin \theta {\tan }^2\theta }$?

Find the definite integral from 1 to 3 of |-3x+1| dx

Determine convergence / divergence of $\sum \sin \frac{\pi }{n^2}$.
Let $a_n=\sin \frac{\pi }{n^2}$.
I attempted the integral test but on the interval $[1,\sqrt{2})$ it is increasing and decreasing on $(\sqrt{2},\mathrm{\infty })$. So the integral test in only applicable for the decreasing part. + the integral computation seems to lead to 3 pages of steps...
I believe the comparison test would be the most reasonable test, graphically I observed that $a_n$ behaves like $b_n=1/n$ when n is large.
$\sum b_n=\mathrm{\infty }$; but, since $b_n>a_n⟹$ inconclusive for divergence/convergence.
I attempted the limit comparison, and ratio test, but inconclusive. I am uncertain if I am doing them properly.
How could I bound below $a_n$ to proceed with the comparison test? Is there a more appropriate method? How would you proceed?

Evaluate the definite integral.
${\displaystyle 2{\int }_0^1(y+1)\sqrt{1-y}dy}$

Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:
${\displaystyle 21m^2+13mn+2n^2}$

Integrate $\frac{9\sqrt{{\tan }^{-1}(3x)}}{7(9x^2+1)}$ with respect to x.