Inverse Trigonometric Functions ITF 2023-2024

Inverse trigonometric functions (ITF) syllabus for 2023 & 2024

• No changes from 2023 syllabus, height and distance removed from trigonometry.
• Everything previously taught is still relevant.

Important ITFs topics based on the last five years of questions (2019-2023)

• Properties of ITFs: 52/100 questions in the last 5 years.
• Equations and Inequalities involving ITFs: 29/100 questions in the last 5 years.
• Series involving ITFs: 19/100 questions in the last 5 years. Only 1 question was asked in 2023.

Topics to focus on:

• Principal Values and Basic Domain & Range:
  • Remember the domain of sin-1x is [-1, 1] and the range is [-π/2, π/2].
  • Remember that the answer of an inverse trigonometric function is always an angle.
• Properties of Inverse trigonometric functions:
  • Make sure to study sum and difference formulas: tan-1 x + tan-1 y, tan-1 x - tan-1 y, sin-1 x - sin-1 y, cos-1 x + cos-1 y.
• Series Involving ITFs
• Trigonometric Substitution
• Interconversion (converting tan-1 to sin-1, cos-1, etc.)

Topics to consider skipping (if time is limited):

• Graphs of ITFs:
  • While understanding the graphs is helpful, focus on understanding how to read values from them.
  • You can consider skipping the graphs of: sin-1 x, cos-1 x, tan-1x, cot-1x, sec-1x, and cosec-1x.
• Graphs of sin-1 (sin x), cos-1 (cos x)
• Formulas: sin-1 x + sin-1 y, cos-1 x + cos-1 y (these have many conditions and may be difficult to apply in a limited time)

Upcoming Trends:

• Domain-based questions:
  • You can expect questions involving finding the domain of ITFs.
• Questions involving principal Values:
  • Familiarize yourself with questions related to finding the principal solution of trigonometric equations.

Solving a tricky example:

• Special question:
  • cot-1(2x) = π + 2cos-1(√(1 - x²))
  • Analyze the ranges of both sides of the equations.
  • Both sides should equal π to satisfy the equation.
  • Substitute π for both sides.
  • Find the values of x that satisfy the equation.
  • If the values of x that satisfy both sides of the equation are different, then no solutions exist.

###  Key takeaway:

• Don't get intimidated by difficult-looking problems.
• Practice as many problems as you can.
• Analyze your strengths and weaknesses.
• Focus on concepts and try to apply them to different problems.
• Track your progress and aim for improvement.

Test your knowledge of Inverse Trigonometric Functions (ITFs) based on the 2023-2024 syllabus. Focus on properties, equations, and inequalities involving ITFs, as well as series associated with them. This quiz will help you understand key concepts and prepare effectively for examinations.