CLASS 11 MATHEMATICS
TRIGONOMETRIC FUNCTIONS
Easy • Detailed • English Medium • Exam Revision Notes
Chapter 3 — explained from basics with examples and memory tricks
1️ What is Trigonometry?
Trigonometry is the study of the relationship between the angles and sides of triangles.
The six trigonometric functions are sin, cos, tan, cosec, sec and cot.
Think: Trigonometry = measuring relationships between angles and sides.
2️ Measuring Angles
Degrees
One complete revolution = 360°. Half revolution = 180°. Quarter revolution = 90°.
Radians
A complete revolution is 2π radians, so:
180° = π radians
90° = π/2 60° = π/3 45° = π/4 30° = π/6
Conversion
Degrees → radians: θ × π/180
Radians → degrees: θ × 180/π
Example: 60° = 60 × π/180 = π/3 radians.
3️ Six Trigonometric Ratios
For a right-angled triangle, relative to angle θ:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
cosec θ = Hypotenuse / Perpendicular = 1/sin θ
sec θ = Hypotenuse / Base = 1/cos θ
cot θ = Base / Perpendicular = 1/tan θ
Remember the first three with SOH–CAH–TOA: Sin = Opposite/Hypotenuse, Cos =
Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
4️ Important Relations
tan θ = sin θ / cos θ
cot θ = cos θ / sin θ
sin θ = 1/cosec θ cos θ = 1/sec θ tan θ = 1/cot θ
These are called reciprocal and quotient relations.
5️ Standard Values
θ 0° 30° 45° 60° 90°
TRIGONOMETRIC FUNCTIONS
Easy • Detailed • English Medium • Exam Revision Notes
Chapter 3 — explained from basics with examples and memory tricks
1️ What is Trigonometry?
Trigonometry is the study of the relationship between the angles and sides of triangles.
The six trigonometric functions are sin, cos, tan, cosec, sec and cot.
Think: Trigonometry = measuring relationships between angles and sides.
2️ Measuring Angles
Degrees
One complete revolution = 360°. Half revolution = 180°. Quarter revolution = 90°.
Radians
A complete revolution is 2π radians, so:
180° = π radians
90° = π/2 60° = π/3 45° = π/4 30° = π/6
Conversion
Degrees → radians: θ × π/180
Radians → degrees: θ × 180/π
Example: 60° = 60 × π/180 = π/3 radians.
3️ Six Trigonometric Ratios
For a right-angled triangle, relative to angle θ:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
cosec θ = Hypotenuse / Perpendicular = 1/sin θ
sec θ = Hypotenuse / Base = 1/cos θ
cot θ = Base / Perpendicular = 1/tan θ
Remember the first three with SOH–CAH–TOA: Sin = Opposite/Hypotenuse, Cos =
Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
4️ Important Relations
tan θ = sin θ / cos θ
cot θ = cos θ / sin θ
sin θ = 1/cosec θ cos θ = 1/sec θ tan θ = 1/cot θ
These are called reciprocal and quotient relations.
5️ Standard Values
θ 0° 30° 45° 60° 90°
