Podcast
Questions and Answers
What is the correct domain of the function sin-1(x)?
What is the correct domain of the function sin-1(x)?
Which sum formula is correct for inverse trigonometric functions?
Which sum formula is correct for inverse trigonometric functions?
Which of the following statements about the range of cos-1(x) is true?
Which of the following statements about the range of cos-1(x) is true?
What is a recommended approach when preparing for examinations involving ITFs?
What is a recommended approach when preparing for examinations involving ITFs?
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When solving the equation cot-1(2x) = π + 2cos-1(√(1 - x²)), what must be true for both sides to be equal?
When solving the equation cot-1(2x) = π + 2cos-1(√(1 - x²)), what must be true for both sides to be equal?
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What is the maximum number of questions involving series with ITFs that were asked in the last five years?
What is the maximum number of questions involving series with ITFs that were asked in the last five years?
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What is the primary focus when studying properties of inverse trigonometric functions?
What is the primary focus when studying properties of inverse trigonometric functions?
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Which graphs may be skipped if time is limited during preparation for ITFs?
Which graphs may be skipped if time is limited during preparation for ITFs?
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Study Notes
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:
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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.
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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):
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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:
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Domain-based questions:
- You can expect questions involving finding the domain of ITFs.
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Questions involving principal Values:
- Familiarize yourself with questions related to finding the principal solution of trigonometric equations.
Solving a tricky example:
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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.
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Description
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.
