Consider the angles and

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Consider the angles

\theta=\dfrac{7\pi}{6}

and

\phi=\dfrac{5\pi}{3}

. Use these values to answer the questions below. (i) Find the reference angle for each of

\theta

and

\phi

. (ii) Hence determine the exact values of

\sin\theta

and

\cos\phi

. (iii) Calculate the numerical values of (a)

S=\sin\theta+\cos\phi

and (b)

P=\tan\theta\,\tan\phi

. State the sign of each result and justify it briefly.