>>7If I told you, you'd probably misuse this feature. I am only using it for academic posts, not random shitposting. I taught myself
\(\large \LaTeX\) in college even though it wasn't taught in any of my classes. Very useful though.
\(\huge Hyperbolic \; functions\)\(\Large Definition:\)Hyperbolic sine of x:
\(\large \sin h x = \frac{e^{x}-e^{-x}}{2}\)Hyperbolic cosine of x:
\(\large \cos h x = \frac{e^{x}+e^{-x}}{2}\)Hyperbolic tangent:
\(\large \tan h x = \frac{\sin h x}{\cos h x}\)Hyperbolic cotangent:
\(\large \cot h x = \frac{\cos h x}{\sin h x}\)Hyperbolic secant:
\(\large \sec h x = \frac{1}{\cos h x}\)Hyperbolic cosecant:
\(\large \csc h x = \frac{1}{\sin h x}\)\(\Large Hyperbolic \; identities\)\(\sin h (-x) = - \sin h x\)\(\cos h (-x) = \cos h x\)\(\cos h^{2} (x) - \sin h^{2} (x) = 1\)\(\large Derivatives \; of \; hyperbolic \; functions\)\(\frac{d}{dx}\sin hx =\cos hx\)\(\frac{d}{dx}\cos hx =\sin hx\)\(\frac{d}{dx}\tan hx =\sec h^{2}x\)\(\frac{d}{dx}\sec hx =- \sec hx \tan hx\)\(\frac{d}{dx}\cot hx =- \csc h^{2}hx\)\(\frac{d}{dx}\csc hx =- \csc hx \cot hx\)Note that some of the signs here are different compared to regular functions and their derivatives.