Topic Details (Notes format)

How to Use Basic Identities for Hyperbolic Functions (sinh, cosh, tanh)

Subject: Mathematics

Book: Maths Mastery

Hyperbolic functions share structural similarities with trigonometric functions but revolve around exponential definitions: sinh(x)=(e^x–e^(–x))/2, cosh(x)=(e^x+e^(–x))/2. Identities like cosh²(x)–sinh²(x)=1 hold. Tanh(x)=sinh(x)/cosh(x). These appear in advanced physics (relativity), engineering (structural forms), or math (hyperbolas). For instance, in a suspended cable (catenary shape), y=a cosh(x/a). Recognizing hyperbolic identity parallels fosters easy transitions between trig and hyperbolic problem-solving and deeper expansions in calculus or geometric modeling.

Practice Questions

What is the sum of the first 10 positive even numbers?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If a square has a perimeter of 64 cm, what is its area?

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What is the square root of 0.25?

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What is the sum of all angles in a hexagon?

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If x^2 - 6x + 9 = 0, what is the value of x?

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The area of an equilateral triangle with side length 6 cm is:

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What is the sum of the first 50 positive integers?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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