Suppose (x ) is an angle satisfying ( x = - 4 13 ) and ( < x < 3 2 ).

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Suppose

x

is an angle satisfying

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

and

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

. (i) Find all six trigonometric ratios of

x

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

E = \sec x - \cot x

leaving your answer as a single rational fraction.