Consider the point $(x,y)=$(1, $\sqrt{3}$) plotted in the graph below.

(a) Find the value of $r$ in the equivalent $(r,\theta)$ polar coordinates.

(b) Now that we have the values of $x$, $y$, and $r$, which of the following equations could help us solve for $\theta$?

A. $\cos(\theta)=\frac{y}{r}$

B. $r\tan(\theta)=\frac{y}{x}$

C. $\sin(\theta)=\frac{x}{r}$

D. $\tan(\theta)=\frac{y}{x}$

E. $\cos(\theta)=\frac{x}{r}$

F. $r\tan(\theta)=\frac{x}{y}$

G. $\tan(\theta)=\frac{x}{y}$

H. $\sin(\theta)=\frac{y}{r}$

I. None of the above

(c) Use one of your answers to part (b) to find a possible value of $\theta$ between 0 and $2\pi$.

(d) Which of the following are also possible values of $\theta$?

A. $\frac{7\pi}{3}$

B. $\frac{5\pi}{3}$

C. $\frac{4\pi}{3}$

D. $\frac{2\pi}{3}$

E. $-\frac{5\pi}{3}$

F. None of the above

(e) Find all possible values of $\theta$.
$\theta=$ + $\cdot k$
where $k$ is any integer and the base angle is between 0 and $2\pi$.

Hint: