The Negativity

Real Values versus The Negativity

Real numbers are the only assertive and straight forward values. When we talk of negative numbers, the figures might work in different way when we indulge towards quantum dynamics. And it is known 10^-xx… gives the precision values i.e., it is denoted in any common scientific values. The value -2 x -2 may not be 4 or -4 in a given system. Rather it might be a different value altogether. To get the actual value involved in the system, it requires complex calculation. Along with it, I feel it is more relevant to have relevant ratio here. If you see the first quadrantt all the trigonometry ratio values are always positive. And all other 3 quadrants has either x-axis or y-axis negativity, so it is imaginative or either it could be transitive.

 

Few Notes

 The trigonometric equations always talks about the ratio of the right angled triangle Ɵ=90. However this ratios are the base for deriving any radical calculations. Refer 

 

http://trythissolution.wordpress.com/article/three-random-points-triangle-circle-14aqr8lbuwpu8-12/
 

SinƟ = opposite_side / hypotenuse
CosƟ = adjacent_side / hypotenuse
TanƟ = opposite_side / adjacent_side
CosecƟ = 1 / SinƟ
SecƟ = 1/CosƟ
CotƟ = 1/TanƟ

Arc Tangents i.e., Inverse trigonometric functions:
Example:
y=Sinx; Sin^-1y=x
Sin45 = 1/(root)2
Sin^-11/(root)2=45
 

Inverse functions:
 

ArcsinƟ=Sin^-1Ɵ
ArccosƟ=Cos^-1Ɵ
ArctanƟ=Tan_^-1Ɵ
ArccosecƟ=Cosec^-1Ɵ
ArcsecƟ=Sec^-1Ɵ
ArccotƟ=Cot^-1Ɵ
 

Conic Section – Hyper bola – Hyperbolic Equations -The ratios for hyperbola

Sinh Cosh Tanh Cosech Sech Tanh and their inverse functions. Please refer http://en.wikipedia.org/wiki/Hyperbolic_function
 

For regular trigonometric functions:

Here, the angle is from the first quadrant x axis anti-clockwise.
 

Also keep this in mind the system may behave anti-trigonometrical, where you may need to refer Vector kind calculations for negativity, here symbol i suppresses the negativity. Or straight forward calculation itself works out. Or some other type mathematical calculation involved.
Also refer http://en.wikipedia.org/wiki/Negativity

Trigonometrical Ratios Sign Values

Quadrant	SinƟ	CosƟ	TanƟ	CoecƟ	SecƟ	CotƟ
1st Quad	+	+	+	+	+	+
2ndQuad	+	-	-	+	-	-
3rdQuad	-	-	+	-	-	+
4thQuad	-	+	-	-	+	-