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Inverse Trigonometric Functions — Study Plan

OJEE · Mathematics

Step-by-step Inverse Trigonometric Functions study plan for OJEE Mathematics 2026 — structured month-wise approach to mastering this chapter.

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A clear, organized comparison chart summarizing the domain and principal value range for all six inverse trigonometric functions: arcsin, arccos, arctan, arccosec, arcsec, and arccot.
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How to Study Inverse Trigonometric Functions

A structured approach to studying Inverse Trigonometric Functions for OJEE Mathematics.

Study Plan for Inverse Trigonometric Functions

1

Day 1–2: Learn the Theory

Study the chapter thoroughly. Note down definitions, formulas, and key concepts.

2

Day 3: Practice Problems

Solve practice questions and previous year OJEE problems. There are 254 questions available for this chapter.

3

Day 4: Revise & Test

Revise key formulas and concepts without looking at notes. Take a practice quiz to test your understanding.

What to Focus On

  • Domain of sin⁻¹x and cos⁻¹x: [-1, 1]
  • Domain of tan⁻¹x and cot⁻¹x: All real numbers (R)
  • Domain of sec⁻¹x and cosec⁻¹x: R - (-1, 1) or |x| ≥ 1

  • sin⁻¹(-x) = -sin⁻¹(x) [odd function]
  • cos⁻¹(-x) = π - cos⁻¹(x)
  • tan⁻¹(-x) = -tan⁻¹(x) [odd function]

  • tan⁻¹x + tan⁻¹y = tan⁻¹((x+y)/(1-xy)) when xy < 1
  • sin⁻¹x + sin⁻¹y = sin⁻¹(x√(1-y²) + y√(1-x²)) when x²+y² ≤ 1
  • cos⁻¹x + cos⁻¹y = cos⁻¹(xy - √(1-x²)√(1-y²)) when x+y ≥ 0

Common Mistakes to Avoid

sin⁻¹(sin x) = x for all real values of x

The range of tan⁻¹x is [0, π] like cos⁻¹x

sin⁻¹x + cos⁻¹x = π/2 for all real x

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Frequently Asked Questions

What topics are covered in Inverse Trigonometric Functions for OJEE?
Inverse Trigonometric Functions is an important chapter in OJEE Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Basic Concepts and Definitions, Properties and Identities, Solving Equations with Inverse Trigonometric Functions, Graphical Properties and Analysis.
How important is Inverse Trigonometric Functions for OJEE?
Inverse Trigonometric Functions is a frequently tested chapter in OJEE Mathematics. Questions from this chapter appear regularly in previous year papers. There are 254 practice questions available for this chapter.
How to prepare Inverse Trigonometric Functions for OJEE?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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