Mathematics

Problem

Suppose

x

is an angle satisfying

\cos x = -\dfrac{4}{13}

and

\pi < x < \dfrac{3\pi}{2}

. a. (i) Find all six trigonometric ratios of

x

. b. (ii) Using the values obtained, simplify the expression

E = \sec x - \cot x

leaving your answer as a single rational fraction.