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