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Trigonometric Functions

Punjab Board · Class 11 · Mathematics

Quick revision notes for Trigonometric Functions — Punjab Board Class 11 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

42 questions26 flashcards5 concepts

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A diagram illustrating the definition of an angle as a measure of rotation, showing the initial side, terminal side, and vertex. It clearly distinguishes between positive (anti-clockwise) and negative
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Key Topics to Revise

1

Angles – Degree and Radian Measure

  • An angle is the measure of rotation of a ray from its initial position (initial side) to its final position (terminal side). The fixed point is called the vertex.
  • Anticlockwise rotation gives a POSITIVE angle. Clockwise rotation gives a NEGATIVE angle.
  • One complete revolution = 360° = 2π radians.
2

Trigonometric Functions via Unit Circle

  • A unit circle has centre at origin O and radius = 1. For any point P(a, b) on the unit circle with angle AOP = x radians (measured from positive x-axis), we DEFINE: cos x = a (x-coordinate) and sin x
  • Since P lies on the unit circle: a² + b² = 1, giving the fundamental identity: sin²x + cos²x = 1.
  • The other four functions are defined as: tan x = sin x / cos x, cot x = cos x / sin x, sec x = 1 / cos x, cosec x = 1 / sin x.
3

Signs and Values of Trig Functions in All Quadrants

  • Quadrant I (0 < x < π/2): ALL trig functions are POSITIVE.
  • Quadrant II (π/2 < x < π): Only SIN and COSEC are positive. All others are negative.
  • Quadrant III (π < x < 3π/2): Only TAN and COT are positive. All others are negative.
4

Trigonometric Identities – Sum and Difference Formulas

  • These are the MOST IMPORTANT formulas in this chapter. Virtually every proof and evaluation question uses them.
  • Core Sum Formulas: sin(x+y) = sin x cos y + cos x sin y. cos(x+y) = cos x cos y – sin x sin y. tan(x+y) = (tan x + tan y)/(1 – tan x tan y).
  • Core Difference Formulas: sin(x–y) = sin x cos y – cos x sin y. cos(x–y) = cos x cos y + sin x sin y. tan(x–y) = (tan x – tan y)/(1 + tan x tan y).

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Full Notes

Key Concepts

An angle is formed by rotatingThe radian is a unitUsing a unit circle (radius =For y = sin xThe unit circle is divided into

Frequently Asked Questions

What are the important topics in Trigonometric Functions for Punjab Board Class 11 Mathematics?
Key topics in Trigonometric Functions include Trigonometric Functions - Comprehensive Overview, Trigonometric Functions - Concept Overview, Flowchart showing how angles are formed through ray rotation and how the direction determines the sign of the angle. These are the concepts Punjab Board Class 11 examiners draw on most — study them first, then practise related questions.
How to score full marks in Trigonometric Functions — Punjab Board Class 11 Mathematics?
Understand the core concepts first, then work through the 42 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All 5 chapters — Punjab Board Class 11 Mathematics Revision Notes

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