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Trigonometry

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This is a informative presentation on trigonometry and its identities. – PowerPoint PPT presentation

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Title: Trigonometry


1
ITS ALL ABOUT TRIGONOMETRY
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2
TRIGONOMETRY FUNCTIONS
FUNCTION ABBREVIATION DESCRIPTION
SINE SIN OPPOSITE/HYPOTENUSE
COSINE COS ADJACENT/HYPOTENUSE
TANGENT TAN OPPOSITE/ADJACENT
COTANGENT COT ADJACENT/OPPOSITE
SECANT SEC HYPOTENUSE/ADJACENT
COSECANT COSEC HYPOTENUSE/OPPOSITE
3
RECIPROCAL IDENTITIES
? sin(a) I/cosec(a) ? cos(a) 1/sec(a) ?
tan(a) 1/cot(a) sin(a)/cos(a) ? cot(a)
1/tan(a) cos(a)/sin(a) ? sec(a) 1/sec(a) ?
cosec(a) 1/cosec(a)
4
PYTHAGOREAN IDENTITIES
  • sin2(a) cos2(a) 1
  • tan2 (a) 1 sec2(a)
  • 1 cot2(a) cosec2(a)

5
ANGLE SUM AND DIFFERENCE TRIGONOMETRY FORMULAE
  • sin(a ß) sin(a)cos(ß) cos(a)sin(ß)
  • sin(a ß) sin(a)cos(ß) cos(a)sin(ß)
  • cos(a ß) cos(a)cos(ß) sin(a)sin(ß)
  • cos(a ß) cos(a)cos(ß) sin(a)sin(ß)
  • tan(a ß) tan(a) tan(ß) / 1 -
    tan(a)tan(ß)
  • tan(a ß) tan(a) - tan(ß) / 1
    tan(a)tan(ß)

6
PRODUCTS AS SUM FORMULAE
sin cos ß     ½sin ( ß) sin ( - ß)
  • sin(a)cos(ß) ½sin(a ß) sin(a ß)
  • cos(a)sin(ß) ½sin(a ß) - sin(a ß)
  • cos(a)cos(ß) ½cos(a ß) cos(a ß)
  • sin(a)sin(ß) -½cos(a ß) - cos(a ß)

7
DOUBLE ANGLE FORMULAE
  • sin(2a) 2sin(a)cos(a)
  • cos(2a) cos2(a) - sin2(a) 1 - 2sin2(a)
    2cos2(a) - 1
  • tan(2a) 2tan(a) / 1 - tan2(a)

8
HALF ANGLE FORMULAE
9
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10
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