Mathematics

Problem

Answer the following with reference to angles in the first quadrant. a. (a) Define the unit circle and state how the coordinates of a point on it are related to

\sin \theta

and

\cos \theta

for an angle

\theta

. b. (b) Complete the following table by writing the exact values (in simplest rationalised radical form) of

\sin \theta

and

\cos \theta

for

\theta = 0^{\circ},\,30^{\circ},\,45^{\circ},\,60^{\circ},\,90^{\circ}

. c. (c) For each of the above angles, write the corresponding coordinate pair

(\cos \theta,\,\sin \theta)

on the unit circle.

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