Question

Find the numerical value of each expression. (Round your answers to five decimal places.) (a) cosh(9) (b) cosh(ln(9))

Answer 1

Answer:

a) $\cosh 9 \approx 4051.54203$, b) $\cosh (\ln 9) \approx 4.55556$.

Step-by-step explanation:

a) As we remember, hyperbolic cosine is represented by the following expression:

$\cosh x = \frac{e^{x}+e^{-x}}{2}$

$\cosh x = \left(\frac{1}{2\cdot e^{x}}\right) \cdot (e^{2\cdot x}+1)$

The numerical value of $\cosh 9$ is:

$\cosh 9 = \left(\frac{1}{2\cdot e^{9}} \right)\cdot (e^{18}+1)$

$\cosh 9 \approx 4051.54203$

b) By using the definition presented and developed in item a), we get the following expression:

$\cosh x = \left(\frac{1}{2\cdot e^{\ln 9}}\right) \cdot (e^{2\cdot \ln 9}+1)$

Now, we simplify this by using power and logarithm properties:

$\cosh (\ln 9) = \left[\frac{1}{(2)\cdot (9)} \right]\cdot (9^{2}+1)$

$\cosh (\ln 9) = \frac{82}{18}$

$\cosh (\ln 9) = \frac{41}{9}$

$\cosh (\ln 9) \approx 4.55556$