Refined and Comprehensive Class 10 Mathematics Notes
Trigonometric Ratios & Core Concepts
Trigonometric ratios express the relationship between the acute angles and sides of a right-angled triangle.
Primary Trigonometric Ratios
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
Reciprocal Ratios
cosec θ = 1 / sin θ = Hypotenuse / Perpendicular
sec θ = 1 / cos θ = Hypotenuse / Base
cot θ = 1 / tan θ = Base / Perpendicular
Fundamental Trigonometric Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Points to Remember
Quotient Identities: Expressing tan and cot in terms of sin and cos is crucial for proving identities: tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.
Value Constraints: The values of sin θ and cos θ never exceed 1, because the hypotenuse is always the longest side in a right-angled triangle.
Important Practice Questions
If sin θ = 3/5, find all other trigonometric ratios for angle θ.
Prove a trigonometric identity using fundamental identities.
Evaluate an expression involving standard angles (0°, 30°, 45°, 60°, 90°).