Mathematics

Problem

A ray starting from the positive

x

–axis is rotated clockwise through

135^{\circ}

to reach a point

P

on the unit circle. Let the angle of rotation be

\theta

(measured from the positive

x

–axis in the standard position). a. (i) Express

\theta

in radians. b. (ii) Determine the coordinates of the point

P

. c. (iii) Hence calculate

\sin\theta

\cos\theta

\tan\theta

\sec\theta

\csc\theta

and

\cot\theta

. d. (iv) Confirm numerically that

\tan\theta\,\cot\theta=1

for this angle.