Trigonometric Ratios - SS1 Mathematics Past Questions and Answers - page 1

If \(\tan\theta = \frac{4}{3}\)

\[\cot\theta = \frac{1}{\tan\theta} = \frac{3}{4}\]

\[\sqrt{\frac{cot\theta}{\tan\theta}} = \ \sqrt{\frac{3}{4} \div \frac{4}{3}} = \ \sqrt{\frac{3}{4} \times \frac{3}{4}} = \sqrt{\frac{9}{16}} = \ \frac{3}{4}\]

1. \(\cos{3\theta} = \sin{2\theta}\)

\[\sin(90{^\circ} - 3\theta) = \sin{2\theta}\]

\[90{^\circ} - 3\theta = 2\theta\]

\[90{^\circ} = 2\theta + 3\theta\]

\[90{^\circ} = 5\theta\]

\[\theta = \frac{90{^\circ}}{5} = 18{^\circ}\]

\(\sin{150{^\circ}} = \sin{(180 - 150)} = \sin{30{^\circ}} = \frac{1}{2}\)