Hyperbolic Functions and Identities

This video tutorial covers common identities related to hyperbolic functions, including even-odd identities, Pythagorean identities, double angle formulas, power reducing formulas, and sum and difference formulas. It also explains how to convert hyperbolic functions into exponential form and vice versa, highlighting the similarities and differences with trigonometric functions.

What is the nature of the hyperbolic sine function?

• Odd

• Both

• Neither

• Even

Which identity is true for hyperbolic cosine?

• cosh(-x) = -sinh(x)

• cosh(-x) = sinh(x)

• cosh(-x) = cosh(x)

• cosh(-x) = -cosh(x)

What is the hyperbolic equivalent of the trigonometric identity cos²x + sin²x = 1?

• cosh²x - sinh²x = 1

• cosh²x + sinh²x = 0

• cosh²x + sinh²x = 1

• cosh²x - sinh²x = 0

How does the hyperbolic identity for tangent differ from the trigonometric one?

• It uses a division

• It uses a multiplication

• It uses a minus sign

• It uses a plus sign

What is the double angle formula for hyperbolic sine?

• sinh²(x) + cosh²(x)

• 2 sinh(x) cosh(x)

• 2 sinh²(x)

• sinh(x) + cosh(x)

Which formula is used to reduce the power of hyperbolic sine?

• sinh²(x) = 1 - cosh(2x)/2

• sinh²(x) = -1 - cosh(2x)/2

• sinh²(x) = 1 + cosh(2x)/2

• sinh²(x) = -1 + cosh(2x)/2

In the sum and difference formulas, how does the sign behave for hyperbolic sine?

• The sign is always negative

• The sign is inverted

• The sign remains the same

• The sign is always positive

What is the sum formula for hyperbolic cosine?

• cosh(x) cosh(y) - sinh(x) sinh(y)

• sinh(x) sinh(y) - cosh(x) cosh(y)

• cosh(x) cosh(y) + sinh(x) sinh(y)

• sinh(x) cosh(y) + cosh(x) sinh(y)

How is hyperbolic sine expressed in terms of exponential functions?

• (e^x - e^(-x))/4

• (e^x + e^(-x))/4

• (e^x - e^(-x))/2

• (e^x + e^(-x))/2

What is the exponential form of hyperbolic tangent?

• (e^x - e^(-x))/(e^x + e^(-x))

• (e^x - e^(-x))/(e^x - e^(-x))

• (e^x + e^(-x))/(e^x + e^(-x))

• (e^x + e^(-x))/(e^x - e^(-x))