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

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What is the value of x if 3x + 7 = 16?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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If the radius of a circle is doubled, what happens to its area?

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