# JavaScript (ES7), 98 bytes

Probably not the golfiest formulas, especially for edge cases.

Returns `[atan(x), asin(x), acos(x)]`.

<!-- language-all: lang-javascript -->

    x=>[(p=1.571,g=x=>v=1/x?x/(h=k=>2*++k-1+(k>>9?0:k*k*x*x/h(k)))``:p)(x),p-2*g((1-x*x)**.5/++x),2*v]

[Try it online!][TIO-llzexkyn]

[JavaScript (Node.js)]: https://nodejs.org
[TIO-llzexkyn]: https://tio.run/##ZU9Nb8IwDL3zK6wewEnaNOn40JgSTtsf4IiQiAqUUNZUbVVF2vbbuxRxYJql@D3bT8/x1fSmzRtbd0nljqfhrAav9A5rJfliJeNChbJXMvUbn@JFlUpnlLEykQxLrV83Yl3Sknrq0wuWhJDDYV0T9CSuk4wWiDIJM0IpX6SMhXZG@/2Qu6p1txO/uQIjAPDwDWA6U8GdtPZBctdG5G3yR56MwZJH/COjfidikDEk4QmejWk@pmVoCb6451UMYRC4HLUBsxGF2POza95NfkEPSsPXBOB5u@ed23aNrQokvDbHbWeaDucEGMzCj2cBz@F4/mlqxD4GS0YXtKBBwHQaDtUgYQNRlZoI1tAHvw/rT0d8IU@Gy1Bcna3wbkrI5IcMvw "JavaScript (Node.js) – Try It Online"

### Formulas

The arctangent is approximated with the continued fractions:

$$\arctan(x)=\dfrac{x}{1+\dfrac{(1x)^2}{3+\dfrac{(2x)^2}{5+\dfrac{(3x)^2}{7+\ddots}}}}$$

We then use:

$$\arccos(x)=2\arctan\left(\frac{\sqrt{1-x^2}}{1+x}\right)$$

and:

$$\arcsin(x)=\frac{\pi}{2}-\arccos(x)$$