Since trigonometrical functions are periodic functions, solutions of trigonometric equations can be generalized with the help of the periodicity of the trigonometrical functions. The solution consisting of all possible solutions of a trigonometric equation is called its general solution.
Trignometry table
We use the following formulae for solving the trigonometric equations:
sin θ = 0 ⇒ θ = nπ,
cos θ = 0 ⇒ θ = (2n + 1)
,
tan θ = 0 ⇒ θ = nπ,
sin θ = sin α ⇒ θ = nπ + (–1)nα, where α ∈ [–π/2, π/2]
cos θ = cos α ⇒ θ = 2nπ ± α, where α ∈ [ 0, π]
tan θ = tan α ⇒ θ = nπ + α, where α ∈ ( –π/2, π/2)
sin2 θ = sin2 α , cos2 θ = cos2 α, tan2 θ = tan2 α ⇒ θ = nπ ± α,
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