QUESTION 6 Simplify the following expressions without using a calculator. \( \begin{array}{l}6.1 \quad \frac{\sin 210^{\circ} \cos 300^{\circ} \tan 240^{\circ}}{\cos 120^{\circ} \tan 150^{\circ} \sin 330^{\circ}} \\ 6.2 \\ {[\sin (-\theta)+\cos (360-\theta)]\left[\cos (90-\theta)+\frac{\sin \theta}{\tan \theta}\right]} \\ 6.3 \text { If } \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \text { and } m^{2}+\frac{1}{m^{2}}=1 \\ \text { Calculate the value of } x \text { without the use of a calculator. }\end{array} \)

(22) If ABC is a triangle in which : \( 5 \sin \mathrm{~A} \sin \mathrm{~B}=6 \sin \mathrm{~B} \sin \mathrm{C}=9 \sin \mathrm{C} \sin \mathrm{A} \), then \( \mathrm{m}(\angle \mathrm{C})= \) \( \begin{array}{llll}\text { (a) } 28 & \text { (b) } 32 & \text { (c) } 36 & \text { (d) } 42\end{array} \) (23) If ABC is a triangle in which \( \cdot 6 a=4 h=3 c \), then the measure of the smallest

5.2 Determine the following with the aid of a calculator 5.2.1 \( \quad \) the size of the angle \( \alpha \). 5.2.2 the area of the \( \triangle P O X \) if it given that \( \mathrm{X}(2 ; 0) \)

\( \sin ^ { T } x + \frac { \sin ^ { T } x } { 1 - \sin ^ { T } x } = \tan ^ { T } x \)

3. Find the radian measure of each angle below: \( \begin{array}{llll}\text { (a) } 35^{\circ} & \text { (b) } 80^{\circ} & \text { (c) } 145^{\circ} & \text { (d) } 220^{\circ}\end{array} \)

If \( \tan \frac{a}{b}=1 \), then \( \tan \frac{2 a}{3 b}=\ldots \ldots \ldots \ldots \) \( \begin{array}{llll}\text { (a) } \frac{1}{2} & \text { (b) } \frac{1}{\sqrt{3}} & \text { (c) } \frac{2}{3} & \text { (d) } \sqrt{3}\end{array} \)