Trigonometric Equations

Mathematics Class XI Chapter 3: Trigonometric Functions Trigonometric Equations

$\to$ The solutions in the interval $[0,2\pi)]$ are called Principal solutions.

$\to$ The solutions of equations the considered over $R$ are called General solutions.

Some Standard Equations:

Equation	Solutions
(i) $\sin x=0$	$x=n \pi, n \in Z$
(ii) $\cos x=0$	$x=(2n+1)\dfrac{\pi}{2}, n \in Z$
(iii) $\sin x= \sin \alpha$	$x=(-1)^n \alpha+n \pi, n \in Z$
(iv) $\cos x=\cos \alpha$	$n=2n \pi \pm \alpha, n\in Z$
(v) $\tan x=0$	$x=n \pi, n \in Z$
(vi) $\tan x=\tan \alpha$	$x=n \pi+\alpha, n \in Z$

where $\alpha$ is a constant.