Use your calculator to compute the values of arcsin($x$) for several different values of $x$. Take note of what range of values you get and what quadrants they lie in.

(a) What quadrants do the values of arcsin$(x)$ seem to lie in?

A. III

B. I

C. II

D. IV

E. None of the above

(b) What are the limitations of using your calculator to find all angles $\theta$ between 0 and $2\pi$ such that $\sin(\theta)=.3$?

A. The calculator's arcsine button will never give you the angles $\theta$ in quadrants II or III.

B. The calculator will only give you outputs between 0 and $2\pi$.

C. The calculator's arcsine button will never tell you the angles $\theta$ in quadrants II, III, or IV.

D. There are two such angles $\theta$, but your calculator can only give you one angle.

E. The calculator's arcsine button will never tell you the angles $\theta$ in quadrants III or IV.

F. None of the above

(c) Is there a similar limitation for using the arccosine function on your calculator to find values of $\theta$ between 0 and $2\pi$ with $\cos(\theta)=.7$?

A. The calculator's arccosine button will never tell you the angles $\theta$ in quadrants II or III.

B. Yes. Again, the calculator will only give you outputs between 0 and $2\pi$.

C. The calculator's arccosine button will never tell you the angles $\theta$ in quadrants II, III, or IV.

D. Yes. Again, there are two such angles $\theta$, but your calculator can only give you one angle.

E. No. There is a unique value of $\theta$ between 0 and $2\pi$ such that $\cos(\theta)=.7$.

F. None of the above