3.13: Tan given: cos, sin, sec + cot

0606/12/F/M/25 — Question 6 · 5 marks

It is given that

\mathrm{tan}\,\theta = \dfrac{\sqrt{5}}{5}

and

180^{\circ} < \theta < 360^{\circ}

(a)

Find the value of

\mathrm{cos}\,\theta

[2]

(b)

Find the value of

\mathrm{sin}\,\theta

[1]

(c)

Find the value of

\mathrm{sec}\,\theta + \mathrm{cot}\,\theta

. Give your answer in the form

\dfrac{a + b\sqrt{c}}{\sqrt{5}}

, where

a

b

and

c

are integers.

[2]