Q21P - Mathematical Methods in Physical Sciences

Question

Use a computer to plot graphs of sinh(x), cosh(x), and tanh(x).

Step-by-Step Solution

Answer

The Graph of cosh(x) is shown below.

The Graph of is shown below.

The Graph of is shown below.

Step 1: Given Information.

The given expression is $\cos h\left(x\right),\sin h\left(x\right),\tan h\left(x\right)$.

Step 2: Definition of Complex Number and Hyperbolic functions.

The domain of a function refers to the range of values that can be plugged into it. This is the set of x values in a function like $\mathit{f}\left(x\right)$. The range of a function is the set of values that the function can take. This is the set of values that the function produces when we enter x value. The values are what you're looking for.

The basic hyperbolic functions are:

1. Hyperbolic sine(sinh)
2.  Hyperbolic cosine(cosh)
3. Hyperbolic tangent(tanh)

Step 3: Plot the graph of c o s h ( x ) , sin h ( x ) , tan h ( x ) .

$cosh\left(x\right)=\frac{e^x+e^{-x}}{2}$

The Graph of cosh(x) is shown below.

$sinh\left(x\right)=\frac{e^x-e^{-x}-x}{2}$

The Graph of$\sin h\left(x\right)$is shown below.

$tanh\left(x\right)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$

The Graph of$\sin h\left(x\right)$is shown below.