Circular R←X○Y
Y must be numeric. X must be an integer in the range ¯12 ≤ X ≤ 12. R is numeric.
X determines which of a family of trigonometric, hyperbolic, Pythagorean and complex functions to apply to Y, from the following table. Note that when Y is complex, a and b are used to represent its real and imaginary parts, while θ represents its phase.
| (-X) ○ Y | X | X ○ Y |
|---|---|---|
(1-Y*2)*.5 | 0 | (1-Y*2)*.5 |
Arcsin Y | 1 | Sine Y |
Arccos Y | 2 | Cosine Y |
Arctan Y | 3 | Tangent Y |
Y=¯1:0Y≠¯1:(Y+1)×((Y-1)÷Y+1)*0.5 | 4 | (1+Y*2)*.5 |
Arcsinh Y | 5 | Sinh Y |
Arccosh Y | 6 | Cosh Y |
Arctanh Y | 7 | Tanh Y |
-8○Y | 8 | (-1+Y*2)*0.5 |
Y | 9 | a |
+Y | 10 | |Y |
Y×0J1 | 11 | b |
*Y×0J1 | 12 | θ |
Examples
0 ¯1 ○ 1
0 1.570796327
1○(PI←○1)÷2 3 4
1 0.8660254038 0.7071067812
2○PI÷3
0.5
9 11○3.5J¯1.2
3.5 ¯1.2
9 11∘.○3.5J¯1.2 2J3 3J4
3.5 2 3
¯1.2 3 4
¯4○¯1
0