Mathematics

Problem

Let

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

be a point on the unit circle. The point

Q

is the reflection of

P

in the

y

–axis. (i) Write the coordinates of

Q

in terms of

\cos \theta

and

\sin \theta

. (ii) State the measure (in terms of

\theta

) of the angle whose terminal side passes through

Q

. (iii) Using the results of parts (i) and (ii), prove that

\sin(\pi-\theta)=\sin \theta \quad\text{and}\quad \cos(\pi-\theta)= -\cos \theta.

(iv) Hence write the exact coordinates of the point on the unit circle corresponding to an angle of

150^{\circ}