2015年6月2日 · I know that $$\sin(x)=\frac{e^{ix}-e^{-ix}}{2i}$$ Then substituting $x=iy$: $$\sin(iy)=\frac{e^{i(iy)}-e^{-i(iy)}}{2i}=\frac{e^{-y}-e^{y}}{2i}$$ Then, according to my lecture …

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle …

How to show $$\sin(x+iy)=\sin(x) \cosh(y) + i\cos(x) \sinh(y)$$ I begin with $$\sin(x+iy) = \frac{e^{x+iy}-e^{-x-iy}}{2i} = \frac{e^xe^{iy}-e^{-x}e^{-iy}}{2i}$$ $$ = \frac{e^xe^{iy}-e^{ …

If x = sinh y, then y = sinh-1 a is called the inverse hyperbolic sine of x. Similarly we define the other inverse hyperbolic functions. The inverse hyperbolic functions are multiple-valued and as …

双曲正弦函数是 双曲函数 的一种。 双曲正弦函数在 数学语言 上一般记作 sinh，也可简写成sh。 与 三角函数 一样，双曲函数也分为双曲正弦、双曲余弦、 双曲正切 、双曲余切、双曲正割、 …

2013年8月9日 · Calculate the integral $\cos(x) \cosh(y) + i \sin(x) \sinh(y)$ 1 Complex analysis: find and sketch the image of the line $y=\sinh^{−1}(2)$ under the mapping $w=\sin(z)$.

解释一下就是：我们先得到一个三角恒等式，然后把里面的sin或者cos全部转为sinh或cosh，如果在公式中出现两个sin相乘，那么把前面的符号改成负号。 上面也给了一个例子，是关于cos …

求 cos(x+iy),sin(x+iy) 的实部和虚部，其中 x,y\\in R. 求解过程如下： cos(x+iy)=cosxcosiy-sinxsiniy=cosxcoshy-isinxsinhy. sin(x+iy)=sinxcosiy+cosxsiniy=sinxcoshy+icosxsinhy

Express \sinh(x+y) and \cosh(x+y) in terms of \cosh(x), \sinh(x), \cosh(y), \sinh(y) https://math.stackexchange.com/questions/1249327/express-sinhxy-and-coshxy-in-terms-of …

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