1. ## Hyperbolic function questions

Hi

I need help on the following questions:

1) Express sinh(x+y) in terms of sinh(x), sinh(y), cosh(x), cosh(y)

2) Given cosh $\displaystyle u=\frac{5}{4}$ find values of sinh(u)

This is what i have done:

made $\displaystyle u=\frac{5}{4}$

so sinh(u) = 1.89.

What is wrong??

P.S

2. Originally Posted by Paymemoney
Hi

I need help on the following questions:

1) Express sinh(x+y) in terms of sinh(x), sinh(y), cosh(x), cosh(y)

2) Given cosh $\displaystyle u=\frac{5}{4}$ find values of sinh(u)
You need to know the following:

$\displaystyle sinh(x) = \frac{e^x - e^{-x}}{2}$ $\displaystyle cosh(x) = \frac{e^x + e^{-x}}{2}$

$\displaystyle e^x = \cosh{x} + \sinh{x}$

$\displaystyle \cosh{(-x)} = \cosh{x}$

$\displaystyle \sinh{(-x)} = -\sinh{x}$
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1)$\displaystyle sinh(x+y) = \frac{e^{x+y} - e^{-(x+y)}}{2} = \frac{e^{x}e^{y} - e^{-x}e^{-y}}{2} =$ $\displaystyle 1/2[(\cosh{x}+\sinh{x})(\cosh{(y)}+\sinh{(y)})$ $\displaystyle - (\cosh{(-x)}+\sinh{(-x)})(\cosh{(-y)}+\sinh{(-y)})]=$ $\displaystyle \sinh{x} \cosh {y} + \cosh{x} \sinh{y}$

2) Is the question: Given,

$\displaystyle cosh(u) = \frac{e^{u} + e^{-u}}{2} =5/4?$

Or is it $\displaystyle u=5/4?$

3. Originally Posted by Anonymous1
2) Is the question: Given,

$\displaystyle cosh(u) = \frac{e^{u} + e^{-u}}{2} =5/4?$
its given like that ^^

4. Originally Posted by Paymemoney
its given like that ^^
In that case sub this identity:

$\displaystyle e^x = \cosh{x} + \sinh{x}$

into the definition of cosh, set it equal to 5/4, and put the whole thing in terms of sinh.

5. Originally Posted by Paymemoney
[snip]

2) Given cosh $\displaystyle u=\frac{5}{4}$ find values of sinh(u)

This is what i have done:

made $\displaystyle u=\frac{5}{4}$

so sinh(u) = 1.89.

What is wrong??

P.S
Several approaches are possible. The simplest is to use the identity $\displaystyle \cosh^2 u - \sinh^2 u = 1$.

6. this is what i have done, someone tell me if this is a correct way of doing it

$\displaystyle \frac{(cosh(u)+sinh(u))+(cosh(-u)+sinh(-u))}{2} = \frac{5}{4}$

$\displaystyle 10 = 4(cosh(u)+sinh(u))+(cosh(-u)+sinh(-u))$

$\displaystyle 2.5 = 2cosh(u)$

$\displaystyle 1.25 = \frac{1}{sinh(u)}$

$\displaystyle sinh(u) = \frac{1}{1/1.25} = 0.8$ my answer is slighlty difference to the book's answers of $\displaystyle \pm0.75$.