Some results which are useful for solving trigonometric equations:

Some results which are useful for solving trigonometric equations:

1) sin θ = sina and cosθ = cosa ⇒ θ = 2nπ + a

2) sin θ = 0 ⇒ θ = nπ

3) cosθ = 0 ⇒ θ = (2n + 1)π/2

4) tan θ = 0 ⇒ θ = nπ

5) sinθ = sina⇒ θ = nπ + (-1)na where a ∈ [–π/2, π/2]

6) cosθ= cos a ⇒ θ = 2nπ ± a, where a ∈[0,π]

7) tanθ = tana⇒ θ = nπ+ a, where a ∈[–π/2, π/2]

8) sinθ = 1 ⇒ θ= (4n + 1)π/2

9) sin θ = -1 ⇒ θ = (4n - 1) π /2

10) sin θ = -1 ⇒ θ = (2n +1) π /2

11) |sinθ| = 1⇒ θ =2nπ

12) cosθ = 1 ⇒ θ =(2n + 1)

13) |cosθ| = 1⇒ θ =nπ