Class 11, Lecture Notes - Trigonometric Functions, Trigonometric Functions

Class 11: Trigonometric Functions – Lecture Notes

Date: November 3, 2019Author: ICSE CBSE Mathematics Student-Assistant 0 Comments

Trigonometric Identities

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

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

$1 + \cot^2 x = \mathrm{cpsec}^2 x$ 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.

	$\sin$	$\cos$	$\tan$	$\mathrm{cosec} x$	$\sec$	$\cot$
$-x$	$- \sin x$	$\cos x$	$- \tan x$	$-\mathrm{cosec} x$	$\sec x$	$-\cot x$
$\frac{\pi}{2}$ $- x$	$\cos x$	$\sin x$	$\cot x$	$\sec x$	$\mathrm{cosec} x$	$\tan x$
$\frac{\pi}{2}$ $+ x$	$\cos x$	$- \sin x$	$- \cot x$	$\sec x$	$-\mathrm{cosec} x$	$-\tan x$
$\pi - x$	$\sin x$	$-\cos x$	$- \tan x$	$\mathrm{cosec} x$	$-\sec x$	$-\cot x$
$\pi + x$	$- \sin x$	$-\cos x$	$\tan x$	$-\mathrm{cosec} x$	$-\sec x$	$\cot x$
$\frac{3\pi}{2}$ $- x$	$-\cos x$	$- \sin x$	$\cot x$	$-\sec x$	$-\mathrm{cosec} x$	$\tan x$
$\frac{3\pi}{2}$ $+ x$	$-\cos x$	$\sin x$	$- \cot x$	$-\sec x$	$\mathrm{cosec} x$	$-\tan x$
$2\pi - x$	$- \sin x$	$\cos x$	$- \tan x$	$-\mathrm{cosec} x$	$\sec x$	$-\cot x$
$2\pi + x$	$\sin x$	$\cos x$	$\tan x$	$\mathrm{cosec} x$	$\sec x$	$\cot x$

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