Problem

Give clear reasons for each of your answers. a. (a) Explain why both

\sin\theta

and

\cos\theta

are positive for every angle

\theta

that lies between

0^{\circ}

and

90^{\circ}

. b. (b) Using a geometric argument on the unit circle, describe how the numerical value of

\sin\theta

changes as

\theta

increases from

0^{\circ}

90^{\circ}

. Why does

\cos\theta

show the opposite trend over the same interval? c. (c) Without performing numerical calculations, determine whether

\tan\theta

is increasing or decreasing on the interval

0^{\circ}<\theta<90^{\circ}

. Justify your answer geometrically.