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Trigonometric Functions - I

NIOS · Class 12 · Mathematics

Quick revision notes for Trigonometric Functions - I — NIOS Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

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Key Topics to Revise

1

Circular Measure of Angles: Degrees and Radians

  • An angle is formed by the rotation of a ray from its initial position to its final position.
  • Anticlockwise rotation gives a positive angle; clockwise rotation gives a negative angle.
  • A unit circle is a circle with radius equal to 1 unit.
2

Trigonometric Functions Using the Unit Circle

  • For any point P(x, y) on the unit circle corresponding to angle θ, we define: sin θ = y, cos θ = x.
  • The coordinates of P can also be written as (cos θ, sin θ).
  • tan θ = y/x (defined when x ≠ 0), cot θ = x/y (defined when y ≠ 0).
3

Trigonometric Values of Standard Angles

  • The values of sin and cos at 0, π/6, π/4, π/3, π/2 must be memorised perfectly.
  • Memory trick for sin values: sin 0 = √(0/4), sin π/6 = √(1/4), sin π/4 = √(2/4), sin π/3 = √(3/4), sin π/2 = √(4/4). Simplify to get 0, 1/2, 1/√2, √3/2, 1.
  • Cosine values are the reverse: cos 0 = 1, cos π/6 = √3/2, cos π/4 = 1/√2, cos π/3 = 1/2, cos π/2 = 0.
4

Graphs of Trigonometric Functions

  • Graph of y = sin θ: starts at 0, rises to maximum 1 at π/2, returns to 0 at π, falls to minimum -1 at 3π/2, returns to 0 at 2π. It is continuous and wave-shaped.
  • Graph of y = cos θ: starts at maximum 1 at θ=0, falls to 0 at π/2, reaches minimum -1 at π, rises to 0 at 3π/2, returns to 1 at 2π. It is also continuous and wave-shaped.
  • Graph of y = tan θ: increases from 0 to +∞ in (0, π/2), then from -∞ to 0 in (π/2, π). Has vertical asymptotes at θ = π/2 and 3π/2. Discontinuous.

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Key Concepts

An angle is formed by rotatingA degree (°) measures an angleWhen an angle θ (in radians)A unit circle (radius = 1)Since (x

Frequently Asked Questions

What are the important topics in Trigonometric Functions - I for NIOS Class 12 Mathematics?
Trigonometric Functions - I covers several key topics that are frequently asked in NIOS Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Trigonometric Functions - I — NIOS Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

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