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📝 Why They Are Called Hyperbolic Functions
📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 16 questions available
Practice MCQs for Why They Are Called Hyperbolic Functions. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.
🔄 Last updated: 2026-07-16
📝 Sample Questions
Q1. Why are the functions \( \sinh x \) and \( \cosh x \) termed 'hyperbolic'?
🔹 A. Because they parametrize a unit hyperbola similar to how sine and cosine parametrize a unit circle
🔹 B. Because they grow faster than exponential
🔹 C. Because they are defined only for hyperbolic angles
🔹 D. Because they solve the hyperbolic differential equation
💡 Difficulty: easy | ✅ Correct: A
Q2. Which identity mirrors the Pythagorean identity for trigonometric functions?
🔹 A. \( \cosh^{2}x + \sinh^{2}x = 1 \)
🔹 B. \( \cosh^{2}x - \sinh^{2}x = 0 \)
🔹 C. \( \cosh^{2}x - \sinh^{2}x = 1 \)
🔹 D. \( \sinh^{2}x - \cosh^{2}x = 1 \)
💡 Difficulty: medium | ✅ Correct: C
Q3. Prove the identity \( \cosh^{2}x - \sinh^{2}x = 1 \) using the definitions of \( \sinh x\) and \( \cosh x\) in terms of exponentials.
🔹 A. By differentiating both sides
🔹 B. By using the unit circle
🔹 C. By numerical approximation
🔹 D. By substituting \( \sinh x = \frac{e^{x}-e^{-x}}{2}\) and \( \cosh x = \frac{e^{x}+e^{-x}}{2}\) and simplifying
💡 Difficulty: hard | ✅ Correct: D
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