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

If the average of five consecutive odd numbers is 25, what is the largest number?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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What is the sum of all even numbers between 1 and 50?

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If x:y = 2:3 and z:y = 4:3, what is x:z?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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What is the length of the diagonal of a square with a side length of 7 cm?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If a number is divisible by 9, it is also divisible by which of the following?

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What is the HCF of 48 and 180?

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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