Mathematics chapters
  1. 013D Geometry
  2. 02Application of Derivatives
  3. 03Area Under Curves
  4. 04Binomial Theorem
  5. 05Circles
  6. 06Complex Numbers
  7. 07Continuity & Differentiability
  8. 08Definite Integration
  9. 09Determinants
  10. 10Differential Equations
  11. 11Ellipse
  12. 12Hyperbola
  13. 13Indefinite Integration
  14. 14Inequalities & Modulus
  15. 15Inverse Trigonometric Functions
  16. 16Limits
  17. 17Logarithms
  18. 18Matrices
  19. 19Methods of Differentiation
  20. 20Number System & Basics
  21. 21Parabola
  22. 22Permutations & Combinations
  23. 23Probability
  24. 24Properties of Triangle
  25. 25Quadratic Equations
  26. 26Sequences & Series
  27. 27Sets, Relations & Functions
  28. 28Statistics
  29. 29Straight Lines
  30. 30Trigonometric Equations
  31. 31Trigonometric Ratios & Identities
  32. 32Vectors

Chapter 30 · Class 11-12 & JEE Main/Adv

Trigonometric Equations

25 topics in 7 parts

Full lessonClass 11 Mathematics · Trigonometric Functions
General Solution of sin x = 0 General Solution of cos x = 0 General Solution of tan x = 0 General Solution of sin x = sin α General Solution of cos x = cos α General Solution of tan x = tan α

Key ideas

+Y +Z +X O(0,0,0) Line L A(x₁, y₁, z₁) a P(x, y, z) r Parallel Vector b = aî + bĵ + ck̂ Cartesian Form: (x - x₁)/a = (y - y₁)/b = (z - z₁)/c = λ ⟺ General Point: (x₁ + λa, y₁ + λb, z₁ + λc)
Trigonometric Equations

Analytical Comparison & Distinction Matrix

Analytical MethodStandard RepresentationParametric / Invariant Framework
Algebraic NatureExplicit equations relating spatial coordinatesParameterized using scalar parameters (λ, μ) or vectors
Symmetry UsageRelies on coordinate expansionExploits vector dot/cross products for rapid simplification
Computational EfficiencyDirect for intercept evaluationSuperior for angles, orthogonal projections, and distances
Common MistakeSign confusion in determinantsOmitting boundary condition checks

All 25 topics in Trigonometric Equations

  1. Trigonometric Equations

    • Principal Solution of a Trigonometric Equation
    • General Solution of a Trigonometric Equation
    • General Solution of Elementary Equations
    • Solution or Root of a Trigonometric Equation

  2. General Solution of Some Standard Equations

    • Equations Based on Critical Values
    • Equations of Form sin θ = sin α
    • Equations of Form tan θ = tan α
    • Equations of Form sin²θ = sin²α or cos²θ = cos²α
    • Equations of Form tan²θ = tan²α
    • Equations of Form a cos θ + b sin θ = c
    • Quadratic & Higher Degree Trigonometric Equations

  3. Solutions in an Interval

    • Number of Solutions in a Given Interval
    • Counting Roots of Trigonometric Equations
    • Parameter Range for Existence of Solutions

  4. Solving Equations Using Graphs

    • Graphical Method for Number of Solutions
    • Intersection of Trigonometric Graphs

  5. System of Simultaneous Equations

    • Simultaneous Trigonometric Equations
    • Ordered Pairs of Solutions

  6. Inequalities

    • Trigonometric Inequations
    • Conditions Holding for All Real x
    • Range of Expression

  7. Special Types of Trigonometric Equations

    • Exponential Trigonometric Equations
    • Logarithmic Trigonometric Equations
    • Equations Involving Absolute Values & Special Functions
    • Equations Using Product & Sum Formulas