Mathematics

Problem

An angle

\phi

satisfies

\sec\phi=\dfrac{13}{12}

and

-\dfrac{\pi}{2}<\phi<0

. a. (i) Determine

\cos\phi

and

\sin\phi

with their proper signs. b. (ii) Hence find

\tan\phi

\csc\phi

, and

\cot\phi

. c. (iii) Using the above results, evaluate

\sin(2\phi)

and

\cos(2\phi)

. Express each answer as a rational number or a rational multiple of a square root, wherever possible.