A Collection of trig and hyper Functions¶
List of Functions¶
Trigonometric functions
- cos
- sin
- tan
Inverse trigonometric functions
- acos
- asin
- atan
Hyperbolic functions
- cosh
- sinh
- tanh
Inverse hyperbolic functions
- acosh
- asinh
- atanh
Type Rules¶
Without complex numbers
bool -> f32
i8 -> f32
i16 -> f32
i32 -> f32
i64 -> f64
f32 -> f32
f64 -> f64
_ -> domain error
With complex numbers
bool -> f32
i8 -> f32 / complex
i16 -> f32 / complex
i32 -> f32 / complex
i64 -> f64 / complex
f32 -> f32 / complex
f64 -> f64 / complex
complex -> f64 / complex
_ -> domain error
Table of trig Functions (ELI)¶
trig(n,x)
- trigonometric functions
nis an integer
| n | x | n | x |
|---|---|---|---|
| 0 | \sqrt{1-x^2} | ||
| -1 | arcsin(x) | 1 | sine(x) |
| -2 | arccos(x) | 2 | cosine(x) |
| -3 | arctan(x) | 3 | tangent(x) |
| -4 | \sqrt{-1+x^2} | 4 | \sqrt{1+x^2} |
| -5 | arcsinh(x) | 5 | sinh(x) |
| -6 | arccosh(x) | 6 | cosh(x) |
| -7 | arccosh(x) | 7 | tanh(x) |
| -8 | -trig(8,x) | 8 | -\sqrt{-1-x^2} for x \ge 0 |
| \sqrt{-1-x^2} for x \lt 0 | |||
| -9 | x | 9 | real(x) |
| -10 | +x | 10 | absolute(x) |
| -11 | x\cdot i | 11 | imaginary(x) |
| -12 | e^{x\cdot i} |