The equations containing trigonometric functions of unknown angles are known as trigonometric equations.

**Trigonometric equations**

The equations containing
trigonometric functions of unknown angles are known as trigonometric equations.
A solution of trigonometric equation is the value of unknown angle that
satisfies the equation. Unless the domain is restricted, the trigonometric
equations have infinitely many solutions, a fact due to the periodicity of
trigonometric functions. Some of the equations may not have a solution at all.

**General
Solution**

The solution of a trigonometric equation
giving all the admissible values obtained with the help of periodicity of a
trigonometric function is called the **general solution** of the equation.

**Principal
Solution**

The smallest numerical
value of unknown angle satisfying the equation in the interval [0*,*
2*Ï€*]
(or) [*âˆ’Ï€, Ï€*] is called a principal solution. We shall take the interval [ *âˆ’Ï€, Ï€*] for defining the principal solution. Further, in this interval we may have two solutions.
Even though both are valid solutions, we take only the numerically smaller one.
This helps us to define the principal domain of the trigonometric functions in
order to have their inverses.

Tags : Definition, Formula, Solved Example Problems, Exercise | Mathematics , 11th Mathematics : UNIT 3 : Trigonometry

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11th Mathematics : UNIT 3 : Trigonometry : Trigonometric equations | Definition, Formula, Solved Example Problems, Exercise | Mathematics

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