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 rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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

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

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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A cube has a side length of 4 cm. What is its volume?

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What is the LCM of 15 and 20?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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The LCM of 12 and 15 is:

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