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Trigonometric Functions - I — Concept Maps

NIOS · Class 12 · Mathematics

3 concept maps of Trigonometric Functions - I for NIOS Class 12 Mathematics, each also written out as a text outline.

45 questions25 flashcards9 formulas & key relations5 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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One of 8 illustrations for Trigonometric Functions - I in Super Tutor — alongside flashcards, concept maps and practice questions.

3 Concept Maps

Complete Chapter Overview: Trigonometric Functions - I

Complete Chapter Overview: Trigonometric Functions - I

The map in words

  • Trig Functions I
    • Angle Measurement
      • Degree
        • 1 degree = pi div 180 rad
        • 360 deg = full circle
      • Radian
        • 1 rad = 180 div pi deg
        • 2pi rad = 360 deg
      • Arc Formula
        • l = r theta
        • theta must be in radians
    • Standard Angles
      • 0 deg zero
      • 30 deg pi div 6
      • 45 deg pi div 4
      • 60 deg pi div 3
      • 90 deg pi div 2
    • Six Trig Functions
      • sin theta = y
      • cos theta = x
      • tan = sin div cos
      • cot = cos div sin
      • sec = 1 div cos
      • cosec = 1 div sin
    • Identities
      • sin sq + cos sq = 1
      • sec sq = 1 + tan sq
      • cosec sq = 1 + cot sq
    • Quadrant Signs
      • Q1 All positive
      • Q2 Sin positive
      • Q3 Tan positive
      • Q4 Cos positive
    • Graphs
      • sin theta
        • Range -1 to 1
        • Period 2pi
        • Continuous
      • cos theta
        • Range -1 to 1
        • Period 2pi
        • Continuous
      • tan theta
        • Range all reals
        • Period pi
        • Discontinuous at pi div 2
      • sec theta
        • No values between -1 and 1
        • Period 2pi
      • cosec theta
        • No values between -1 and 1
        • Period 2pi
      • cot theta
        • Range all reals
        • Period pi
    • Periodicity
      • sin cos sec cosec = 2pi
      • tan cot = pi
      • f(bx) period = base div b

Flowchart showing the relationship between degree and radian measures and conversion factors.

Flowchart showing the relationship between degree and radian measures and conversion factors.

The map in words

  • Angle Measurement
    • Degrees
      • 360° = Full Rotation
        • Conversion
          • 1° = π/180
          • 1 rad = 180°/π
    • Radians
      • 2π = Full Rotation

Flowchart showing how to use the arc length formula for different scenarios.

Flowchart showing how to use the arc length formula for different scenarios.

The map in words

  • Problem: Find arc length or angle
    • Given:
      • Radius r and Angle θ: Find Arc Length
        • Use: ℓ = rθ
          • IMPORTANT: θ must be in radians!
      • Arc Length ℓ and Radius r: Find Angle
        • Use: θ = ℓ/r
      • Arc Length ℓ and Angle θ: Find Radius
        • Use: r = ℓ/θ

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Frequently Asked Questions

What are the important topics in Trigonometric Functions - I for NIOS Class 12 Mathematics?
Key topics in Trigonometric Functions - I include Circular Measure of Angles: Degrees and Radians, Trigonometric Functions Using the Unit Circle, Trigonometric Values of Standard Angles, Graphs of Trigonometric Functions. Study these first, then practise questions on each for the NIOS Class 12 board exam.
What do the concept maps for Trigonometric Functions - I show?
The 3 maps show how the ideas in Trigonometric Functions - I connect: Complete Chapter Overview: Trigonometric Functions - I; Flowchart showing the relationship between degree and radian measures and conversion factors.. Each map is also written out as an outline on this page.
How should I revise Trigonometric Functions - I for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Trigonometric Functions - I. Revise 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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