Introduction to Trigonometry Class 10 Mathematics — Revision Notes
Trigonometry studies relationships between angles and sides of triangles. Sine, cosine, and tangent ratios are fundamental tools for solving problems invol
TL;DR: Trigonometry studies relationships between angles and sides of triangles. Sine, cosine, and tangent ratios are fundamental tools for solving problems…
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Trigonometry studies relationships between angles and sides of triangles. Sine, cosine, and tangent ratios are fundamental tools for solving problems invol
Trigonometric Ratios
- sin θ = opposite/hypotenuse
- cos θ = adjacent/hypotenuse
- tan θ = opposite/adjacent = sin θ / cos θ
- cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
Trigonometric Values for Standard Angles
- sin 0° = 0, cos 0° = 1, tan 0° = 0
- sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3
- sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1
- sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3
- sin 90° = 1, cos 90° = 0, tan 90° = undefined
Trigonometric Identities
- sin² θ + cos² θ = 1 (Pythagorean identity)
- sec² θ - tan² θ = 1
- cosec² θ - cot² θ = 1
- sin(90° - θ) = cos θ, cos(90° - θ) = sin θ, tan(90° - θ) = cot θ
Applications of Trigonometry
- Angle of elevation: angle above horizontal when looking up
- Angle of depression: angle below horizontal when looking down
- Solving real-world problems involving heights, distances, and angles
Key Terms
- Trigonometry: Study of relationships between angles and sides of triangles
- Sine: Ratio of opposite side to hypotenuse
- Cosine: Ratio of adjacent side to hypotenuse
- Tangent: Ratio of opposite side to adjacent side
- Angle of Elevation: Angle above horizontal when looking upward
Frequently Asked Questions
What is sin 30°?
sin 30° = 1/2 or 0.5.
How do you remember trigonometric ratios?
Use mnemonic SOH-CAH-TOA: Sin=Opposite/Hypotenuse, Cos=Adjacent/Hypotenuse, Tan=Opposite/Adjacent.
If sin θ = 3/5, what is cos θ?
Using sin² θ + cos² θ = 1: cos² θ = 1 - (3/5)² = 1 - 9/25 = 16/25, so cos θ = 4/5.
More Class 10 Mathematics Revision Notes
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
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