Mathematics

Problem

Let

\theta=-750^{\circ}

be an angle measured clockwise from the positive

x

–axis. a. (i) Express

\theta

as a positive angle between

0^{\circ}

and

360^{\circ}

. b. (ii) Determine the reference angle associated with

\theta

. c. (iii) Using the reference angle, find the signs of

\sin\theta

\cos\theta

and

\tan\theta

. d. (iv) Hence, without using a calculator, write the exact values of

\sin\theta

\cos\theta

and

\tan\theta

. (Use standard values for

30^{\circ}

and

60^{\circ}

where required.)