Monkey Raptor

Saturday, November 16, 2013

Math: List of Trigonometric Identities

Basic Identities : Pythagorean and Ratios

  • sin² A + cos² A = 1
  • tan² A + 1 = sec² A
  • 1 + cot² A = cosec² A
  • tanA = sinA / cosA
  • cosecA = 1 / sinA
  • secA = 1 / cosA
  • cotA = cosA / sinA
    cotA = 1 / tanA

Co-function Identities: Shifts

  • sin[(½)π - A] = cosA
    sin(90° - A) = cosA
  • cos[(½)π - A] = sinA
    cos(90° - A) = sinA
  • tan[(½)π - A] = cotA
    tan(90° - A) = cotA

Odd-Even Identities : Reflection

  • sin(-A) = - sinA
  • cos(-A) = cosA
  • tan(-A) = - tanA

Addition Formulas : Angle Sum and Difference

  • sin(A + B) = sinA·cosB + cosA·sinB
  • sin(A - B) = sinA·cosB - cosA·sinB
  • cos(A + B) = cosA·cosB - sinA·sinB
  • cos(A - B) = cosA·cosB + sinA·sinB
  • tan(A + B) = ( tanA + tanB ) / ( 1 - tanA·tanB )
  • tan(A - B) = ( tanA - tanB ) / ( 1 + tanA·tanB )

Double-Angle Formulas

  • sin2A = 2·sinA·cosA
  • cos2A = cos² A - sin² A
    cos2A = 1 - 2·sin² A
    cos2A = 2·cos² A - 1
  • tan2A = ( 2·tanA ) / ( 1 - tan² A )

Half-Angle Formulas

  • sin²(½A) = (1 - cosA)/2
    sin(½A) = √[( 1 - cosA )/2]
  • cos²(½A) = ( 1 + cosA )/2
    cos(½A) = √[( 1 + cosA )/2]
  • tan(½A) = ( 1 - cosA ) / sinA
    tan(½A) = sinA / ( 1 + cosA )

Product Formulas

  • 2·sinA·cosB = sin(A + B) + sin(A - B)
  • 2·cosA·cosB = cos(A + B) + cos(A - B)
  • 2·cosA·sinB = sin(A + B) - sin(A - B)
  • 2·sinA·sinB = cos(A - B) - cos(A + B)

Factoring Formulas

  • sinA + sinB = 2·cos[ (A - B)/2 ]·sin[ (A + B)/2 ]
  • sinA - sinB = 2·cos[ (A + B)/2 ]·sin[ (A - B)/2 ]
  • cosA + cosB = 2·cos[ (A + B)/2 ]·cos[ (A - B)/2 ]
  • cosA - cosB = - 2·sin[ (A + B)/2 ]·sin[ (A - B)/2 ]
Math: List of Trigonometric Identities
http://monkeyraptor.johanpaul.net/2013/11/list-of-trigonometric-identities.html