Trigonometry — Chapter Summary
Kerala Board · Class 10 · Mathematics
Summary of Trigonometry for Kerala Board Class 10 Mathematics. Key concepts: In 45°, sin θ = opposite and cos θ = adjacent.
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Overview
Trigonometry is the branch of mathematics that deals with the relationships between angles and sides of triangles. In this chapter, we explore special right triangles, introduce trigonometric ratios (sine, cosine, tangent), and learn how to apply these concepts to solve real-world problems involving
Key Concepts
In 45°
In 45°-45°-90° triangles, sides are in ratio 1:1:√2. In 30°-60°-90° triangles, sides are in ratio 1:√3:2 (shortest to longest). These relationships al
sin θ = opposite side/hypotenuse
sin θ = opposite side/hypotenuse in a right triangle. For any angle θ, sine represents the ratio that remains constant regardless of the triangle's si
cos θ = adjacent side/hypotenuse
cos θ = adjacent side/hypotenuse in a right triangle. Represents horizontal components and distances from the angle's vertex. Key values: cos 30° = √3
tan θ = opposite side/adjacent side
tan θ = opposite side/adjacent side = sin θ/cos θ. Represents the slope or steepness of an angle. Key values: tan 30° = 1/√3, tan 45° = 1, tan 60° = √
Angle of elevation is measured upward
Angle of elevation is measured upward from horizontal line of sight. Angle of depression is measured downward from horizontal line of sight. Used with
Learning Objectives
- Understand the relationship between angles and sides in special right triangles (30°-60°-90° and 45°-45°-90°)
- Define and calculate trigonometric ratios: sine, cosine, and tangent
- Apply trigonometric ratios to find unknown sides and angles in right triangles
- Solve real-world problems involving heights and distances using angles of elevation and depression
- Calculate areas of triangles and other polygons using trigonometric methods
Frequently Asked Questions
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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