Consider the following diagram:

(a) Suppose $(x,y)=(24,10).$ What is the value of $r$?

(b) Give a possible value for the angle $A$ between 0 and $2\pi$. Note that there are infinitely many possibilities for $A$ outside this interval.

(c) Suppose we were to consider one of the other three points in the diagram. Would the value of $r$ change? What about the value of $A$? Use symmetry to find the polar coordinates of the other three points. Each angle $A$ should be given in radians between 0 and $2\pi$.
Point Q has polar coordinates

(d) Use your work above to convert the Cartesian coordinates $(-6,8)$ to polar coordinates. [Hint: take note of what quadrant the point is in.]

(e) In general, if $(x,y)$ is an arbitrary point in the first quadrant, how can you find an equivalent polar coordinate $(r,A)$?

A. $A=\arcsin(\frac{y}{r})$ (using calculator)

B. $A=\arccos(\frac{y}{r})$ (using calculator)

C. $r=\sqrt{x^2+y^2}$

D. $A=2\pi-\arcsin(\frac{y}{r})$ (using calculator)

E. $A=\pi-\arcsin(\frac{y}{r})$ (using calculator)

F. $A=-\arcsin(\frac{y}{r})$ (using calculator)

G. $r^2=x^2-y^2$

H. None of the above

What if $(x,y)$ is in the second quadrant?

A. $A=\pi+\arcsin(\frac{y}{r})$ (using calculator)

B. $A=\pi-\arcsin(\frac{y}{r})$ (using calculator)

C. $A=-\arcsin(\frac{y}{r})$ (using calculator)

D. $A=\arcsin(\frac{y}{r})$ (using calculator)

E. $r=\sqrt{x^2+y^2}$

F. $A=2\pi-\arcsin(\frac{y}{r})$ (using calculator)

G. $r^2=x^2-y^2$

H. None of the above