Area of a Triangle, (sides a,b,c).. Area = ( b . c sin A )/ 2

Area of a Triangle , (2s = a + b + c).. Area = Sqrt (a .(s - a). (s - b). (s - c))

Area of a Circle (r = radius).. Area = p . r ²

Area and Volume of a Cylinder

Area and Volume of a Cone

Area and Volume of a Frustrum of a Cone

Area and Volume of a Sphere

Area and Volume of a Pyramid

sin A = Opposite / Hypotenuse = a / c

cosine A = Adjacent / Hypotenuse = b/ c

tangent A = Opposite / Adjacent = a / b

secant A = 1 / sin = c / a

cosecant A = 1/cosine = b / c

cotangent A = 1/tangent. = b / a

sinh x = (e^x - e^-x) / 2

cosh x = (e^x + e^-x) / 2

tanh x = sinh x / cosh x = (e^x - e^-x) / (e^x + e^-x)

sech x = 1 / sinh x = 2 / (e^x - e^-x)

cosech x = 1 / cosh x = 2 / (e^x + e^-x)

coth x = cosh x / sinh x = (e^x + e^-x) / (e^x - e^-x)

sin x = x / 1 - x³/3! + x ⁵/5! - x7 / 7! +

cos x = 1 - x²/2! + x⁴/4! -x ⁶/6!...

e^x = 1 + x / 1 + x²/2! + x³/3! +x ⁴/4!...

sinh x = x / 1! + x³/3! + x ⁵/5! + x7 / 7! +

cosh x = 1 + x²/2! + x⁴/4! +x ⁶/6!...

log(1+ x ) = x - x²/2! + x³/3! - x ⁴/4! + ...

( x + 1)ⁿ = 1 + n . x + n .( n - 1 ) x² / 2! + n .( n - 1 ). ( n - 2 ) x³ / 3! + ...(n / r ) x^r +...

y = sin x ..dy/dx = cos x

y = cos x ..dy/dx = -sin x

y = tan x ..dy/dx = sec² x

y = cotan x ..dy/dx = -cosec² x

y = sec x...dy/dx = sec x. tan x

y = cosec x ...dy/dx = -cosec x. cot x.

Product Rule ...d( u .v ) / dx = u . dv/dx + v . du/dx

Quotient Rule... d( u / v) / dx = (v . du / dx - u . dv / dx ) / v²

F'( x) = f(x)
xa	x a+1 /(a + 1)
1 / (a2 + x2)	(1 / a) . tan -1 (x / a)
1 / x	log | x |
1 / (x . Sqrt (x 2 - a 2)	(1 / a) . sec -1 (x / a)
ex	ex
1 / ( a2- x2)	(1 / a). tanh -1 ( x / a ) = 1 /( 2. a) . log(a + x/a - x )
ax	ax / log a
1 / Sqrt( a2 - x2)	sin -1( x / a )
tan x	log | sec x |
sec x	log | sec x + tan x| = log |tan (x/2 + p /4) |
1 / Sqrt( x2 + a2)	sinh -1( x / a ) = log ( (x/a) +Sqrt(x2 /a2 +1))
cosec x	log | tan x/2 |
+/- 1 /Sqrt( x2 - a2)	cosh -1( x / a)= log ( (x/a) +/- Sqrt(x2 /a2 - 1))

Moments Of Inertia

Parallel axis Theory..
If the second moment of an area (A) about an axis x-x = I_xx. Then the second moment of Area about a parallel axis y-y which is distance x from x-x =