 ## Tutoring on Using the Properties of Hyperbolic Functions

Learning Objectives:

#### Understand to use the Properties of Hyperbolic Functions.

Math Tutoring on Using the Properties of Hyperbolic Functions

Hyperbolic functions are written like the trig functions cos, sin, tan, etc., but have an 'h' at the end, such as cosh(x), sinh(x), and tanh(x). The hyperbolic function f(x) = cosh x is defined by the formula cosh x =(eˣ + e¯ˣ) / 2. The function satisfies the conditions cosh 0 = 1 and cosh x = cosh(−x). The hyperbolic function f(x) = sinh x is defined by the formula sinh x = (eˣ - e¯ˣ) / 2. The function satisfies the conditions sinh 0 = 0 and sinh(−x) = − sinh x. For large values of x the graphs of sinh x and cosh x are close together. For large negative values of x the graphs of sinh x and − cosh x are close together.
Therefore,
tanh x = sinh x / cosh x  = (eˣ - e¯ˣ) / (eˣ + e¯ˣ).

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Hook Questions:

1.    What is hyperbolic sine?

2.    What is Coshx?

3.    Can coshx be zero?

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