Derivatives formulas

Inverse trigonometry formulas

trigonometry formulas

*Length of arc =radius×angle subtends at center
*Conversation between degree  and radian measure
Degree measure = (180°÷π)×radian measure
Radian measure =(π÷180°)×degree measure
Trigonometry ratio
Sin²x + Cos²x=1
Sec²x - tan²x=1
Cosec²x - Cot²x =1
* Signs of trigonometric in quadrant
All trigonometry are positive in 1st quadrant(0° to 90° or 0 to π/2)
All trigonometry are negative except sinx and cosecx in 2nd quadrant (90° to 180° or π/2 to π )
All trigonometry are negative except tan and cotx in 3rd quadrant (180° to 270° or π  to 3π/2)
All trigonometry are negative except cosx and secx (270° to 360° or 3π/2 to 2π)
Sin(-x)= -Sinx
Cos(-x) = Coax
Sec(-x) = Secx
Cosec(-x) = -Cosecx
tan(-x) = -tanx
Cot(-x) = Cotx

Sin(x+y) = SinxCosy +CosxSiny
Sin(x-y) = SinxCosy - CosxSiny
Cos(x+y) = CosxCosy - SinxSiny
Cos(x-y) = CosxCosy + SinxSiny
Sin2x = 2SinxCosx = 2tanx/(1+tan²x)
Cos2x = Cos²x - Sin²x = 2Cos²x-1
             =1-2Sin²x= (1-tan²x)/(1+2tan²x)
tan2x = 2tanx/(1-tan²x)
Sin3x =3Sinx - 4Sin³x
Cos3x = 4Cos³x - 3Cosx
tan3x = (3tanx-tan³x)/(1-3tan²x)

Basic Identities

(x+y)² =x²+2xy+y²
(x-y)² =x²-2xy+y²
(x+a)×(x+b) = x²+(a+b)x+ab
(x-a)×(x-b) = x²-(a+b)x +ab
x²-y² = (x+y)×(x-y)
x²+y²= (x+y)²-2xy = (x-y)²+2xy
(x+y)³ = x³+3x²y+3xy²+y³
(x+y)³ = x³-3x²y+3xy²+y³
x³+y³ =(x+y)(x²-xy+y²)
x³-y³ = (x-y)(x²+xy+y²)
(x+y+z)² = x²+y²+z²+2xy+2yz+2zx
x³+y³+z³-3xyz = (x+y+z)(x²+y²+z²-xy-yz-zx)
x³+y³+z³-3xyz = ½(x+y+z)[(x-y)²+(y-z)²+(z-x)²]
Roots of quadratic equation ax²+bx+c=0
x=[-b±√(b²-4ac)]÷2a

Surface area and volumes

*Surface area of cube :- 6×side²
*Lateral surface area of cube :- 4×side²
*Length of edges of cube :- 12×side
*volume of cube :- side³
*Surface area of cuboid :- 2(l×b+b×h+h×l)
*Lateral surface area of cuboid :- 2(l+b)h
*Length of edges of cuboid :- 4(l+b+h)
*Volume of cuboid :- l×b×h
*Curved surface area of cylinder :- 2πrh
*Total surface area of cylinder :- 2πr(h+r)
*Volume of cylinder :- πr²h
*Curved surface area of cone :- πrl where l=√(r²+h²)
*Total surface area of cone :- πr(l+r)
*Volume of cone :- ⅓πr²h
*Curved surface area of sphere :- 4πr²
*Volume of sphere :- 4/3πr³
*Curved surface area of hemisphere :- 2πr²
*Total surface area of hemisphere :- 3πr²
*Volume of hemisphere :- ⅔πr³
*Curved surface area of frustum of cone :- πl(r1 +r2) where l=√[h²+(r1²-r2²)]
*Total surface area of frustum of cone :- πl(r1+r2)+πr1²+πr2²
*Volume of frustum of cone :- ⅓πh(r1²+r2²+r1×r2)

Area of triangles and trapezium

*Area of right angle triangle:- ½base×perpendicular
*Area of equilateral triangle:- √3/4×side²
*Area of isosceles triangle :- ½×base×height
*Area of triangle (using heron's formula) :- √[s×(s-a)×(s-b)×(s-c)] where a,b,c are the sides of triangle and s=(a+b+c)/2
*Area of parallelogram :- Base×perpendicular
*Area of square :- side²
*Area of rhombus :- ½×d1×d2 where d1=first diagonal and d2 =second diagonal
*Area of trapezium :- ½×(a+b)×h where a,b are length of parallel sides and "h" is height of trapezium