0
votes
2answers
46 views

Is this a typo, or am I missing something?

I have a handout for my precalc II class. It says $\sinh(-x) = -\sin(x)$ It should be $\sinh(-x) = -\sinh(x)$ right? I don't see how a negative input could make a hyperbolic function circular.
0
votes
2answers
30 views

Write the following as an algebraic expression of x; sinh(lnx)

So I have a questions asking for $sinh(log_ex)$ sinh(x) = $\frac{e^x-e^{-x}}{2}$ So $sinh(log_x)$ = $\frac{e^{lnx}-e^{-lnx}}{2}$ $\frac{e^{lnx}-e^{lnx^{-1}}}{2}$ = $\frac{x - x^{-1}}{2}$ ...
2
votes
4answers
98 views

Inverse of $(e^x - e^{-x})/2$

What is the inverse of the function $f(x)=\frac{e^x - e^{-x}}2$? I tried replacing $e^x$ by a variable but I still can't get it.
0
votes
1answer
94 views

Does $e^{i*\theta}$ Relate To Hyperbolic Sine/Cosine?

I would like to understand the relationship betwene $e^{i\cdot \theta}$ and hyperbolic sine and cosine. Here is what I have done so far: Given: $$\sinh(x)+\cosh(x)=e^x $$ ...
0
votes
1answer
52 views

Rewriting a hyperbolic equation in standard form

$9x^2-4y^2-72x$ = 0 How would that be done? So far, I got up to $\frac{9(x^2-8x)}1-\frac{4(y-0)^2}1=0$
2
votes
1answer
148 views

Simplifying $\cosh \mathrm{arcsinh} \ x$

How can I simplify the following: $$\cosh \mathrm{arcsinh} \ x$$ I know that an expression of the form $f(g^{-1}(x))$ where $f$ and $g$ are trigonometric functions can be simplified by constructing a ...
0
votes
1answer
47 views

Need some algebra explaination for hyperbolic sinus

I am reading a book where i have come across an expression: $$ \frac{e^{x}\left(-a^2+b^2+2iab\right)- e^{-x}\left(-a^2 +b^2-2iab\right)}{2} $$ In the book they state that we can express this ...
3
votes
1answer
123 views

Why do we get two solutions when inverting $y = \sinh x$?

Using the definition $\sinh x = \dfrac{e^x-e^{-x}}{2},\;$ let's say we want to solve $\;y = \sinh x \;$ for $x$. It's not hard to show that $\;\sinh x \;$ is bijective, so this should have exactly ...
0
votes
2answers
40 views

How do I show this hyperbolic identity?

I am trying to derive $$y = \exp \left(\dfrac{a+b}2t \right) \left(k_1 \cosh \left(\dfrac{(a-b)t}2 \right) + k_2 \sinh \left(\dfrac{(a-b)t}2 \right) \right)$$ From $$y = c_1 \exp(at) + c_2 ...