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Trigonometric Functions - I

NIOS · Class 12 · Mathematics

Complete topic list for Trigonometric Functions - I in NIOS Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions25 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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4 Topics · NIOS Class 12 Mathematics

Topics in Trigonometric Functions - I

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.

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?
Key topics in Trigonometric Functions - I include Complete Chapter Overview: Trigonometric Functions - I, Flowchart showing the relationship between degree and radian measures and conversion factors., Flowchart showing how to use the arc length formula for different scenarios.. These are the concepts NIOS Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Trigonometric Functions - I — NIOS Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

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

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