Mathematics

Problem

An angle

\theta

satisfies

\sec\theta = -\dfrac{4}{3}

with

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

. Work through the following steps: a. (i) Determine

\cos\theta

and state its sign. b. (ii) Using the value of

\cos\theta

, find

\sin\theta

. c. (iii) Compute

\tan\theta

and

\cot\theta

. d. (iv) Show numerically that

\tan\theta \cdot \cot\theta = 1

for your values.