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| Pi Times |
o. 0 0 0 |
Circle Function
|
o. y yields p 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. 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 p):
1p_1 * _1 _2 o./ _1 1
_0.5 0.5
1 0
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Ndx
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