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Chapter 2: Q21P (page 71)

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

Short Answer

Expert verified

The Graph of cosh(x) is shown below.

The Graph of is shown below.

The Graph of is shown below.

Step by step solution

01

Given Information.

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

02

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 $f (x)$ . 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 enterx value. The values are what you're looking for.

The basic hyperbolic functions are:

Hyperbolic sine(sinh)
Hyperbolic cosine(cosh)
Hyperbolic tangent(tanh)

03

Plot the graph of cosh(x),sinh(x),tanh(x).

$c o s h (x) = \frac{e^{x} + e^{- x}}{2}$

The Graph of cosh(x) is shown below.

$s i n h (x) = \frac{e^{x} - e^{- x} - x}{2}$

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

$t a n h (x) = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}$

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

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Most popular questions from this chapter

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly find $x, y, r, θ$ in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

-4i.

For each of the following numbers, first visualize where it is in the complex plane. With a little practice, you can quickly find $x, y, r, θ$ in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also, plot the complex conjugate of the number.

$7 (c o s 110^{°} - i s i n 110^{°})$ .

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

$\frac{25}{3 + 4 i}$ .

Question: Describe geometrically the set of points in the complex plane satisfying the following equations. .

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

$\frac{z}{\bar{z}}$ .

See all solutions

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