Major centers with nice trigonometric coordinates

X(6149)=X(13)-Isoconjugate of X(14), (the last center published in ETC by Dec 12, 2014) has the very nice barycentrics coordinates F(A) : F(B) : F(C), where F(A) = sin(3*A).

The next table shows other centers with similar simple and nice trigonometric coordinates, when these represent trilinears or barycentrics and when points can be found from other known centers.

F(A)	Center with trilinears F(A):F(B):F(C)	Center with barycentrics F(A):F(B):F(C)
sin(A)	X(6)	X(1)
sin(2*A)	X(48)	X(3)
sin(3*A)	X(50)	X(6149)
sin(4*A)	X(563)	X(1147)
sin(6*A)	(47,48)∩(50,2477)	Complement of X(562) (2,562)∩(3,54)
sin(2*A)^2	(1,1748)∩(31,48)	X(577)
sin(2*A)^3		(3,54)∩(4,2055)
sin(2*A)^4		(577,1147)∩(1971,2055)
sin(3*A)^2	(50,215)∩(1109,2619)	(6,1511)∩(1971,3258)
sin(3*A)^3	(49,50)∩(54,2088)
cos(A)	X(3)	X(63)
cos(2*A)	X(47)	X(1993)
cos(3*A)	X(49)	(48,63)∩(662,2167)
cos(4*A)	Eigencenter of anticevian triangle of X(563) On line (1,1748)	(2,95)∩(50,1993)
cos(A)^2	X(255)	X(394)
cos(A)^3	X(1092)	(48,63)∩(92,1958)
cos(A)^4	(1,775)∩(47,560)	(2,801)∩(32,1993)
cos(2*A)^2	(1,1748)∩(560,2964)	(2,95)∩(32,1994)
tan(A)	X(19)	X(4)
tan(2*A)	X(1820)	X(68)
tan(3*A)		X(562)
tan(A)^2	X(1096)	X(393)
tan(A)^3	Isogonal conjugate of X(1102) (19,158)∩(811,2128)	Isogonal conjugate of X(3964) (4,51)∩(25,393)
tan(A)^4		Polar conjugate of X(4176) (133,3863)∩(185,1208)
tan(2*A)^2		(68,577)∩(216,2165)