Trigonometric Equations

Trigonometric equation: An equation having trigonometric functions is called a trigonometric equation.

Ex : sin θ = 1

sin θ + cos θ =1

tan θ = 1

Trigonometric identity : A trigonometric identity is also an equation which gets satisfied by any value of the unknown quantity.

Ex : sin2θ + cos2θ=1

Key Point: A trigonometric equation is satisfied by finite or infinite specific values of the unknown quantity not by any value of the unknown quantity.

Solution of a trigonometric equation: There are two types of solutions of a trigonometric equation:

I. Principal solution: A solution in which the values of the unknown quantity belong to the interval [0,2π] is called a principal solution.

II. General solution: A solution in which there are infinite values of the unknown quantity is called a general solution.

Important results :

I. sin θ = 0 ⇒ θ = nπ           II. cos θ = 0 ⇒ θ = (2n+1)π/2             III. tan θ = 0 ⇒ θ = nπ

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