o. Pi Times - Circle Function

>> << Ndx Usr Pri Phr Dic Rel Voc !: wd Help Dictionary

Pi Times | o. 0 0 0 | Circle Function

`o. y` yields π times`y` .`` Thus`o. 1` is approximately`3.14159` . |  | The function`x&o.` is even or odd as`x` is even or odd;`(-x)&o.` is its inverse.

x o. y | x |  | (-x) o. y
Sqrt 1-(Sqr y) | 0 |  | Sqrt 1-(Sqr y) | `0&o.@(1&o.)` ↔`2&o.`
Sine y | 1 |  | Arcsine y | Radian arg/result
Cosine y | 2 |  | Arccos y | "
Tangent y | 3 |  | Arctan y | "
Sqrt (Sqr y)+1 | 4 |  | Sqrt (Sqr y)-1 | `4&o.@(5&o.)` ↔`6&o.`
Sinh y | 5 |  | Arcsinh y | Sinh is hyperbolic sine
Cosh y | 6 |  | Arccosh y
Tanh y | 7 |  | Arctanh y
Sqrt - (1 + Sqr y) | 8 |  | - Sqrt - (1 + Sqr y)
RealPart y | 9 |  | y
Magnitude y | 10 |  | Conjugate`` (`+y`)
ImaginaryPart y | 11 |  | `j. y`
AngleOf y | 12 |  | `^j. y`

Examples:

       rfd=: %&180 @ o.            NB. Radians from degrees
       sin=: 1&o.
       SIN=: sin@rfd
       (rfd 0 90 180);(sin 0 1.5708);(SIN 0 90)
    +----------------+---+---+
    |0 1.5708 3.14159|0 1|0 1|
    +----------------+---+---+

The principal domain of the inverse of a non-monotonic function is restricted. The limits on real domains of arcsine and arccos may be obtained as follows (as multiples of π):

       1p_1 * _1 _2 o./ _1 1
    _0.5 0.5
       1   0

>> << Ndx Usr Pri Phr Dic Rel Voc !: wd Help Dictionary