• Gluemotion 1 2 3
• Gluemotion 1 2 3 =

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1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
1	H	He
	1	2
2	Li	Be	B	C	N	O	F	Ne
	2,1	2,2	2,3	2,4	2,5	2,6	2,7	2,8
3	Na	Mg	Al	Si	P	S	Cl	Ar
	2,8,1	2,8,2	2,8,3	2,8,4	2,8,5	2,8,6	2,8,7	2,8,8
4	K	Ca	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn	Ga	Ge	As	Se	Br	Kr
	2,8,8,1	2,8,8,2	2,8,9,2	2,8,10,2	2,8,11,2	2,8,13,1	2,8,13,2	2,8,14,2	2,8,15,2	2,8,16,2	2,8,18,1	2,8,18,2	2,8,18,3	2,8,18,4	2,8,18,5	2,8,18,6	2,8,18,7	2,8,18,8
5	Rb	Sr	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd	Ag	Cd	In	Sn	Sb	Te	I	Xe
	2,8,18 8,1	2,8,18 8,2	2,8,18 9,2	2,8,18 10,2	2,8,18 12,1	2,8,18 13,1	2,8,18 14,1	2,8,18 15,1	2,8,18 16,1	2,8,18 18,0	2,8,18 18,1	2,8,18 18,2	2,8,18 18,3	2,8,18 18,4	2,8,18 18,5	2,8,18 18,6	2,8,18 18,7	2,8,18 18,8
6	Cs	Ba	*	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg	Tl	Pb	Bi	Po	At	Rn
	2,8,18 18,8,1	2,8,18 18,8,2	2,8,18 32,10,2	2,8,18 32,11,2	2,8,18 32,12,2	2,8,18 32,13,2	2,8,18 32,14,2	2,8,18 32,15,2	2,8,18 32,17,1	2,8,18 32,18,1	2,8,18 32,18,2	2,8,18 32,18,3	2,8,18 32,18,4	2,8,18 32,18,5	2,8,18 32,18,6	2,8,18 32,18,7	2,8,18 32,18,8
7	Fr	Ra	**	Rf	Db	Sg	Bh	Hs	Mt	Uun	Uuu	Uub
	2,8,18,32 18,8,1	2,8,18,32 18,8,2	2,8,18,32 32,10,2	2,8,18,32 32,11,2	2,8,18,32 32,12,2	2,8,18,32 32,13,2	2,8,18,32 32,14,2	2,8,18,32 32,15,2	2,8,18,32 32,17,1	2,8,18,32 32,18,1	2,8,18,32 32,18,2
*	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu
2,8,18 18,9,2	2,8,18 20,8,2	2,8,18 21,8,2	2,8,18 22,8,2	2,8,18 23,8,2	2,8,18 24,8,2	2,8,18 25,8,2	2,8,18 25,9,2	2,8,18 27,8,2	2,8,18 28,8,2	2,8,18 29,8,2	2,8,18 30,8,2	2,8,18 31,8,2	2,8,18 32,8,2	2,8,18 32,9,2
**	Ac	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No	Lr
2,8,18,32 18,9,2	2,8,18,32 18,10,2	2,8,18,32 20,9,2	2,8,18,32 21,9,2	2,8,18,32 23,8,2	2,8,18,32 24,8,2	2,8,18,32 25,8,2	2,8,18,32 25,9,2	2,8,18,32 26,9,2	2,8,18,32 28,8,2	2,8,18,32 29,8,2	2,8,18,32 30,8,2	2,8,18,32 31,8,2	2,8,18,32 32,8,2	2,8,18,32 32,9,2

Trigonometric Identities

(Math Trig Identities)

sin(theta) = a / c	csc(theta) = 1 / sin(theta) = c / a
cos(theta) = b / c	sec(theta) = 1 / cos(theta) = c / b
tan(theta) = sin(theta) / cos(theta) = a / b	cot(theta) = 1/ tan(theta) = b / a

sin(-x) = -sin(x)
csc(-x) = -csc(x)
cos(-x) = cos(x)
sec(-x) = sec(x)
tan(-x) = -tan(x)

Gluemotion 1 2 3

cot(-x) = -cot(x)

sin^2(x) + cos^2(x) = 1	tan^2(x) + 1 = sec^2(x)	cot^2(x) + 1 = csc^2(x)
sin(x y) = sin x cos y cos x sin y
cos(x y) = cos x cosy sin x sin y

tan(x y) = (tan x tan y) / (1 tan x tan y)

sin(2x) = 2 sin x cos x

cos(2x) = cos^{^2}(x) - sin^{^2}(x) = 2 cos^{^2}(x) - 1 = 1 - 2 sin^{^2}(x)

tan(2x) = 2 tan(x) / (1 - tan^{^2}(x))

sin^{^2}(x) = 1/2 - 1/2 cos(2x)

cos^{^2}(x) = 1/2 + 1/2 cos(2x)

sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 )

cos x - cos y = -2 sin( (x - y)/2 ) sin( (x + y)/2 )

Trig Table of Common Angles

angle	0	30	45	60	90
sin^2(a)	0/4	1/4	2/4	3/4	4/4
cos^2(a)	4/4	3/4	2/4	1/4	0/4
tan^2(a)	0/4	1/3	2/2	3/1	4/0

Gluemotion 1 2 3 =

Given Triangle abc, with angles A,B,C; a is opposite to A, b opposite B, c opposite C:

a/sin(A) = b/sin(B) = c/sin(C) (Law of Sines)

c^2 = a^2 + b^2 - 2ab cos(C) b^2 = a^2 + c^2 - 2ac cos(B) a^2 = b^2 + c^2 - 2bc cos(A)

(Law of Cosines)

(a - b)/(a + b) = tan [(A-B)/2] / tan [(A+B)/2] (Law of Tangents)