INTRODUCTION TO TRIGONOMETRY - True/False

In a right triangle, if an acute angle is \(\theta\), then \(\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\).

In a right triangle, \(\cos \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\).

For an acute angle \(\tan \theta = \dfrac{\sin \theta}{\cos \theta}\).

The reciprocal of \(\sin \theta\) is \(\sec \theta\).

For any acute angle \(\theta?\) in a right triangle, \(\sin^2 \theta + \cos^2 \theta = 1\).

For any acute angle \(\theta\ \sec^2 \theta - \tan^2 \theta = 1\).

For any acute angle \(\theta\), \(\text{cosec}^2 \theta - \cot^2 \theta = 1\).

\(\tan \theta \cdot \cot \theta = 1\) for any acute angle \(\theta\).

\(\sin 0^\circ = 1\) and \(\cos 0^\circ = 0\).

\(\sin 90^\circ = 1\) and \(\cos 90^\circ = 0\).

\(\sin 30^\circ = \dfrac{1}{2}\) and \(\cos 30^\circ = \dfrac{\sqrt{3}}{2}\).

\(\sin 45^\circ = \dfrac{1}{\sqrt{2}}\) and \(\cos 45^\circ = \dfrac{1}{\sqrt{2}}\).

\(\tan 45^\circ = 1\)

\(\tan 30^\circ = \sqrt{3}\) and\(\tan 60^\circ = \dfrac{1}{\sqrt{3}}\).

\(\sin 60^\circ = \dfrac{\sqrt{3}}{2}\) and \(\cos 60^\circ = \dfrac{1}{2}\).

For any angle \(\theta\) (where defined), \(\tan \theta = \dfrac{\sin \theta}{\cos \theta}\) and \(\cot \theta = \dfrac{\cos \theta}{\sin \theta}\).

For complementary angles, \(\sin (90^\circ - \theta) = \cos \theta\).

For complementary angles, \(\tan (90^\circ - \theta) = \tan \theta\).

For complementary angles, \(\\text{cosec } (90^\circ - \theta) = \sec \theta\) and \(\cot (90^\circ - \theta) = \tan \theta\).

In a right triangle, the hypotenuse is always the longest side.

In a right triangle, for an acute angle \(\theta\), \(\sin \theta\) can be greater than 1.

If sin?\(\sin \theta = \dfrac{3}{5}\) for an acute angle ?\theta?, then cos?\(\cos \theta = \dfrac{4}{5}\).

If \(\cos \theta = \dfrac{5}{13}\) for an acute angle \(\theta\), then \(\sin \theta = \dfrac{12}{13}\).

The trigonometric ratios introduced in Class 10 Chapter 8 are defined only for acute angles of a right triangle.

In Class 10, the standard angles for which exact trig values are usually memorised are \(0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ\).