Identity equation and rule sheet maths equations

What is the first sin rule

Sin x = (180-x)

Second sin rule

Sin x = (x+360)

Third sin rule

Sin(180+x) = sin(-x) = -sinx

First cos rule

Cos x = cos(-x)

Second cos rule

Cos(x+360)

Third cos rule

Cos(180-x) = cos(180+x) = - cos x

Rule for tan

Tan x = tan(x+180) = tan (x+360)

What is the basic identity for adjacent

Adj = hyp*cosx

What is the basic identity for opposite

Opp = hyp*sinx

What is the second basic identity for adjacent

Adj = opp/tanx

What is the basic identity for tanx

Tanx = sinx/cosx

What is the basic identity for sin^2x and cos^2x

Sin^2x + cos^2x = 1

What double angle formula is used to find sin2x

Sin2x = 2sinxcosx

First double angle formula for Cos2x

Cos2x = cos^2x - sin^2x

Second double angle formula used to find Cos2x

2cos^2x - 1

Third double angle formula used to find cos2x

Cos2x = 1-2sin^2x

What double angle formula is used to find tan2x

Tan2x = 2tanx/1-tan^2x

What is the compound angle for sin

Sin(A+/-B) = SinACosB +/- CosASinB

What is the compound angle for cos

Cos(A-/+B) = CosACosB -/+ SinASinB

What is the compound angle for Tan

Tan(A+/-B) = TanA +/- TanB / 1 -/+ TanATanB

What is the reciprocal of Cosec x

CosecX = 1/Sinx

What is the reciprocal of Secx

Secx =1/cosx

What is the reciprocal of Cotx

Cotx=1/tanx

What is the reciprocal of Sec^2x

Sec^2x = 1 + tan^2x

What is the reciprocal of Cosec^2x

Cosec^2x = 1 + cot^2x

What equation is used for arc length

Arc length = theta

What equation is used to find the circumference of a circle

Circumference of circle = 2piR

What equation is used to find the area of a circle

Area of a circle = piR^2

What equation is used to find the curved surface area of a cylinder

Curved surface are of cylinder = 2piRH

What is the equation for the surface are of a sphere

Surface area of sphere = 4piR^2

What equation is used to find the area of a trapezium

Area of trapezium = 1/2(a + b)h

What equation is used to find the volume of a cylinder

Volume of cylinder = piR^2h

What equation is used to find the volume of a sphere

Volume of sphere = 4/3pir^3

Pythagorean Theorem

a^2 + b^2 = c^2

What is the equation for cosine rule

A^2 = B^2 + C^2 - 2bc cosA

What is the equation for sine rule

a/sinA = b/sinB = c/sinC

Algebraic notation of a whole number

3n - 1, 3n, 3n+1

What is the Algebraic notation of Even number

2n

What is the Algebraic notation of an odd number

2n + 1

(a + b)^2 =

a^2 + 2ab + b^2

(a + b)^3 =

a^3 + 3a^2b + 3ab^2 + b^3

What is the first law of indices

a^m * a^n = a^m+n

What is the second law of indices

a^m/a^n = a^m-n

What is the third law of indices

(a^m)^n = a^m*n

What is the fourth law of indices

a^0 = 1

What is the fifth law of indices

a^-n = 1/a^n

What is the sixth law of indices

a^m/n = (sqrt^n a)^m = sqrt^n a^m

What is the first key rule of indices

a^n * b^n = (ab)^n

What is the second law of indices

a^n / b^n = (a/b)^n

what is equation for the difference of two squares

(a + b)(a-b) = a^2 - b^2

Quadratic equation

ax^2+bx+c=0

Second quadratic equation

X = -b +/- sqrt b^2 - 4 ac / 2a

What formula is used for the discriminant

x = b^2 - 4ac

What is the fourth rule for cosx

Cosx = sin(90-x)

What is the fourth rule for sinx

Sinx = cos(90-x)

For 30 degrees what is the angle radian , sin ,cos and tan

angle radian = pi/6 sin = 1/2 cos = sqrt3/2 tan =1/sprt3

For 45 degrees what is the angle radian , sin ,cos and tan

angle radian = pi/4 sin = 1/sprt2 cos = sqrt2/2 tan = 1

For 60 degrees what is the angle radian , sin ,cos and tan

angle radian = pi/3 sin = sqrt3/2 cos = 1/2 tan = sqrt3

For 90 degrees what is the angle radian , sin ,cos and tan

angle radian = pi/2 sin = 1 cos = 0

For 120 degrees what is the angle radian , sin ,cos and tan

angle radian = 2pi/3 sin = sqrt3/2 cos = -1/2 tan = -sqrt3

For 135 degrees what is the angle radian , sin ,cos and tan

angle radian = 3pi/4 sin = 1/sqrt2 cos = - 1/sqrt2 tan = -1

For 150 degrees what is the angle radian , sin ,cos and tan

Angle radian = 5pi/6 sin = 1/2 cos = -sqrt3/2 tan = - 1/sqrt3

For 180 degrees what is the angle radian , sin ,cos and tan

angle radian = pi sin = 0 cos = -1 tan = 0

direct proportion

ratio of two quantities is constant ( F = kx )

inverse proportion

product of two quantities is constant ( y = k/x^2 )

linear functions

closely related to direct proportion

midpoint equation

M = (x1 + x2 - x1/2 , y1 + y2 - y1/2)

except distance equation

D = sqrt (y2 - y1)^2 + (x2 - x1)^2

non vertical straight line

y = mx + c

equation for gradient

m = y2 - y1/x2 -x1

line with gradient passing through

y - y1 = m (x - x1)

parallel

m1 = m2 = m3

perpendicular

m2 = - 1/m1

equation of a circle

(x-a)^2 + (y-b)^2 = r^2

tangent line

one intersection ( = 0)

change > 0

two intersection

change < 0

no intersection

disjoined

d > r1 + r2

tangent

d = r1 + r2

intersect equation one

r2 -r1 < d < r1 + r2

intersect equation two

d = r2 - r1

intersect equation three

d < r2 -r1

arithmetic sequence

Un = a + (n -1)d

arithmetic sequence ( position to term)

Sn = n/2(2a + (n-1)d)

geometric sequence (position to term)

Un = ar^n-1

Geometric sequence ( equation of r is less than or equal to 1)

Sn = a(1-r^n)/1-r

Geometric sequence ( equation of r is greater than 1)

Sn =a(r^n-1)/r-1

infinite geometric sequence

S infinity = a/1-r