We will discuss about the trigonometric equation formula. We need to use the formula to find the general solution or some particular solution of different types of trigonometric equation.
1. If sin θ = 0 then θ = nπ, where n = zero or any integer.
2. If sin θ = sin ∝ then θ = nπ + (-1)\(^{n}\) ∝, where n = zero or any integer.
3. If sin θ = 1 then θ = (4n + 1)\(\frac{π}{2}\), where n = zero or any integer.
4. If sin θ = -1 then θ = (4n - 1)\(\frac{π}{2}\), where n = zero or any integer.
5. If cos θ = 0 then θ = (2n + 1)\(\frac{π}{2}\), where n = zero or any integer.
6. If cos θ = cos ∝ then θ = 2nπ ± ∝, where n = zero or any integer.
7. If cos θ = 1 then θ = 2nπ, where n = zero or any integer.
8. If cos θ = -1 then θ = (2n + 1)π, where n = zero or any integer.
9. If tan θ = 0 then θ = nπ, where n = zero or any integer.
10. If tan θ = tan ∝ than θ = nπ + ∝, where n = zero or any integer.
11. If sin\(^{2}\) θ = sin\(^{2}\) ∝ then θ = nπ ± ∝, where n = zero or any integer.
12. If cos\(^{2}\) θ = cos\(^{2}\) ∝ then θ = nπ ± ∝, where n = zero or any integer.
13. If tan\(^{2}\) θ = tan\(^{2}\) ∝ than θ = nπ ± ∝, where n = zero or any integer.
14. If a cos θ + b sin θ = c then θ = 2nπ + ∝ ± β, where cos β = \(\frac{c}{\sqrt{a^{2} + b^{2}}}\), cos ∝ = \(\frac{a}{\sqrt{a^{2} + b^{2}}}\) and sin ∝ = \(\frac{b}{\sqrt{a^{2} + b^{2}}}\), where n = zero or any integer.
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