Class 11: Trigonometric Functions – Lecture Notes – ICSE / ISC / CBSE Mathematics Portal for K12 Students

Trigonometric Identities

$\cos^2 x + \sin^2 x = 1$

$1 + \tan^2 x = \sec^2 x \text{ for all } x \in R - \Big\{ (2n-1) \frac{\pi}{2} : n \in Z \Big\}$

$1 + \cot^2 x = \mathrm{cosec}^2 x \text{ for all } x \in R - \{ n \pi : n \in Z \}$

Trigonometric Functions in Different Quadrants

$\theta$ lies in Quadrant II

$\sin \theta : +ve$ $\mathrm{cosec} \theta : +ve$

$\cos \theta : -ve$ $\sec \theta : -ve$

$\tan \theta : -ve$ $\cot \theta : -ve$

$\theta$ lies in Quadrant I

$\sin \theta : +ve$ $\mathrm{cosec} \theta : +ve$

$\cos \theta : +ve$ $\sec \theta : +ve$

$\tan \theta : +ve$ $\cot \theta : +ve$

$\theta$ lies in Quadrant III

$\sin \theta : -ve$ $\mathrm{cosec} \theta : -ve$

$\cos \theta : -ve$ $\sec \theta : -ve$

$\tan \theta : +ve$ $\cot \theta : +ve$

$\theta$ lies in Quadrant IV

$\sin \theta : -ve$ $\mathrm{cosec} \theta : -ve$

$\cos \theta : +ve$ $\sec \theta : +ve$

$\tan \theta : -ve$ $\cot \theta : -ve$

The value of the trigonometric functions are given in terms of $x$ in the table below.