Mathematics

Problem

Consider a point

P(a,b)

on the unit circle corresponding to an angle

x

measured from the positive

x

-axis. Answer the following questions. a. (i) Using the coordinates of

P

, prove that

\sin^{2}x+\cos^{2}x=1

. b. (ii) State the maximum and minimum possible numerical values of

\sin x

and

\cos x

and justify your answer based on part (i). c. (iii) If

x

lies in the third quadrant, explain which of

\sin x

and

\cos x

are positive or negative.