Mathematics

Number System Algebra Trigonometry Area Profit and Loss Multiplication Table Square, Square Root & Cube
Basic Trigonometric Function Formulas
  • $sinθ={Opposite Side}/{Hypotenuse}$
  • $cosecθ={Hypotenuse}/{Opposite Side}$
  • $cosθ={Adjacent Side}/{Hypotenuse}$
  • $secθ={Hypotenuse}/{Adjacent Side}$
  • $tanθ={Opposite Side}/{Adjacent Side}$
  • $cotθ={Adjacent Side}/{Opposite Side}$
Reciprocal Identities
  • $sinθ=1/{cosecθ}$
  • $cosecθ={1}/{sinθ}$
  • $cosθ={1}/{secθ}$
  • $secθ={1}/{cosθ}$
  • $tanθ={1}/{cotθ}$
  • $cotθ={1}/{tanθ}$
Cofunction Identities
  • $sin(90°−x) = cos x$
  • $cos(90°−x) = sin x$
  • $tan(90°−x) = cot x$
  • $cot(90°−x) = tan x$
  • $sec(90°−x) = cosec x$
  • $cosec(90°−x) = sec x$
Sum & Difference Identities
  • $sin(x+y) = sin(x)cos(y)+cos(x)sin(y)$
  • $cos(x+y) = cos(x)cos(y)–sin(x)sin(y)$
  • $tan(x+y) = {tan x + tan y}/{1 - tan x . tan y}$
  • $sin(x–y) = sin(x)cos(y)–cos(x)sin(y)$
  • $cos(x–y) = cos(x)cos(y) + sin(x)sin(y)$
  • $tan(x-y) = {tan x - tan y}/{1 + tan x . tan y}$
Double Angle Identities
  • $sin 2x = 2sin x . cos x = {2tan x}/{1 + tan^2 x}$
  • $cos 2x = cos^x - sin^x = {1 - tan^x}/{1 + tan^x}$
  • $cos 2x= 2cos^2x - 1 = 1 - 2sin^2x$
  • $tan 2x = {2tan x}/{1 - tan^2 x}$
  • $sec 2x = {sec^2x}/{2 - sec^2x}$
  • $cosec 2x = {(sec x . cosec x)}/2$
Triple Angle Identities
  • $sin 3x = 3sin x – 4sin^3x$
  • $cos 3x = 4cos^3x-3cos x$
  • $tan 3x = {3tan x - tan^3x}/{1 - 3tan^2x}$
Half Angle Identities
  • $sinx/2 = ±√{{1 - cosx}/{2}}$
  • $cosx/2 = ±√{{1 + cosx}/{2}}$
  • $tanx/2 = √{{1 - cosx}/{1 + cosx}} = {1 - cosx}/{sin x} $
Product identities
  • $sinx . cosy = {sin(x+y)+sin(x-y)}/2$
  • $cosx . cosy = {cos(x+y)+cos(x-y)}/2$
  • $sinx . siny = {cos(x-y)-cos(x+y)}/2$
Sum to Product Identities
  • $sinx + siny = 2sin{x+y}/2 . cos{x-y}/2$
  • $sinx - siny = 2cos{x+y}/2 . sin{x-y}/2$
  • $cosx + cosy = 2cos{x+y}/2 . cos{x-y}/2$
  • $cosx - cosy = -2sin{x+y}/2 . sin{x-y}/2$
Inverse Trigonometry Formulas
  • $sin^{-1} (–x) = – sin^{-1} x$
  • $cos^{-1} (–x) = π – cos^{-1} x$
  • $tan^{-1} (–x) = – tan^{-1} x$
  • $cosec^{-1} (–x) = – cosec^{-1} x$
  • $sec^{-1} (–x) = π – sec^{-1} x$
  • $cot^{-1} (–x) = π – cot^{-1} x$
Trigonometry Table
Angles (In Degrees) 0° 30° 45° 60° 90° 180° 270° 360°
sin 0 1/2 1/√2 √3/2 1 0 -1 0
cos 1 √3/2 1/√2 1/2 0 -1 0 1
tan 0 1/√3 1 √3 ∞ 0 ∞ 0
cot ∞ √3 1 1/√3 0 ∞ 0 ∞
cosec ∞ 2 √2 2/√3 1 ∞ -1 ∞
sec 1 2/√3 √2 2 ∞ -1 ∞ 1