Trigonometry Formulas

Trigonometry Formulas and Table (Class 10 to Class 12)

Trigonometry plays a crucial role in mathematics and physics. Below is a detailed collection of fundamental trigonometry formulas, including identities, function definitions, and a trigonometry table.

Fundamental Trigonometric Function Formulas for Class 10-12

The six primary trigonometric functions are:

• Sine (sin) = Opposite/Hypotenuse
• Cosine (cos) = Adjacent/Hypotenuse
• Tangent (tan) = Opposite/Adjacent
• Cosecant (csc) = 1/sin
• Secant (sec) = 1/cos
• Cotangent (cot) = 1/tan

Key Pythagorean Identities

1. sin²θ + cos²θ = 1
2. 1 + tan²θ = sec²θ
3. 1 + cot²θ = csc²θ

Reciprocal Identities

1. sinθ = 1/cscθ
2. cosθ = 1/secθ
3. tanθ = 1/cotθ
4. cscθ = 1/sinθ
5. secθ = 1/cosθ
6. cotθ = 1/tanθ

Trigonometric Formulas for Sum and Difference of Angles

1. sin(A ± B) = sinA cosB ± cosA sinB
2. cos(A ± B) = cosA cosB ∓ sinA sinB
3. tan(A ± B) = (tanA ± tanB) / (1 ∓ tanA tanB)

Double Angle and Half Angle Formulas

1. sin(2A) = 2 sinA cosA
2. cos(2A) = cos²A – sin²A
3. tan(2A) = (2 tanA) / (1 – tan²A)

For half-angle formulas, use:

1. sin(A/2) = ±√((1 – cosA) / 2)
2. cos(A/2) = ±√((1 + cosA) / 2)
3. tan(A/2) = ±√((1 – cosA) / (1 + cosA))

Trigonometry Table (Common Angles)

Angle (θ)	sinθ	cosθ	tanθ	cotθ	secθ	cscθ
0°	0	1	0	∞	1	∞
30°	1/2	√3/2	1/√3	√3	2/√3	2
45°	1/√2	1/√2	1	1	√2	√2
60°	√3/2	1/2	√3	1/√3	2	2/√3
90°	1	0	∞	0	∞	1

Applications of Trigonometry

Trigonometry has numerous real-life applications, including:

• Engineering and Architecture
• Astronomy and Space Science
• Navigation and GPS
• Physics and Wave Mechanics

Trigonometry Cheat Sheet for Quick Revision

For a quick reference, you can use a Trigonometry Cheat Sheet that summarizes all important formulas, including:

• Basic trigonometric identities
• Reciprocal identities
• Sum and difference formulas
• Double and half-angle formulas
• Common trigonometric values

Download Trigonometry Formulas PDF

To help with your studies, you can download a Trigonometry Formulas PDF that includes all important formulas, tables, and identities in a well-structured format.

Conclusion

Mastering trigonometric formulas is essential for excelling in mathematics. This guide provides a structured approach for Class 10-12 students to understand and apply trigonometry effectively. Keep practicing and refer to this guide whenever needed!

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