Trigonometric Equation Formula

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.

● Trigonometric Equations

• General solution of the equation sin x = ½
• General solution of the equation cos x = 1/√2
• General solution of the equation tan x = √3
• General Solution of the Equation sin θ = 0
• General Solution of the Equation cos θ = 0
• General Solution of the Equation tan θ = 0
• General Solution of the Equation sin θ = sin ∝
  
• General Solution of the Equation sin θ = 1
• General Solution of the Equation sin θ = -1
• General Solution of the Equation cos θ = cos ∝
• General Solution of the Equation cos θ = 1
• General Solution of the Equation cos θ = -1
• General Solution of the Equation tan θ = tan ∝
• General Solution of a cos θ + b sin θ = c
• Trigonometric Equation Formula
• Trigonometric Equation using Formula
• General solution of Trigonometric Equation
• Problems on Trigonometric Equation

11 and 12 Grade Math

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