Trigonometric Formulas – HSC Math

Posted In: Mathematics
  1. In circular system, $θ°={\arc}/{\radius}=s/r$
    or, $s=rθ$
  2. $1 \radian=1 \rad=1^c=(180/π)^°$
  3. Area of a circular sector (symbol ⌔)
    $⌔\AOB=1/2r^2θ$ [θ in radian]
  4. $sin\ θ=1/{cosec\ θ}; cos\ θ=1/{sec\ θ}; tan\ θ=1/{cot\ θ}$
  5. $tan\ θ={sin \θ}/{cos\ θ}; cot\ θ={cos\ θ}/{sin\ θ}$
  6. $sin^2\ θ+cos^2\ θ=1$
  7. $sec^2\ θ-tan^2\ θ=1$
  8. $cosec^2\ θ-cot^2\ θ=1$
  9. $-1≤sin\ θ≤1$
  10. $-1≤cos\ θ≤1$
  11. $cosec\ θ≤-1, 1≤cosec\ θ$
  12. $sec\ θ≤-1, 1≤sec\ θ$
  13. $sin(θ±2πn)=sin θ, \period\ 2π \or\ 360°$
  14. $cos(θ±2πn)=cos θ, \period\ 2π \or\ 360°$
  15. $sec(θ±2πn)=sec θ, \period\ 2π \or\ 360°$
  16. $cosec(θ±2πn)=cosec θ, \period\ 2π \or\ 360°$
  17. $tan(θ±πn)=tan θ, \period\ π \or\ 180°$
  18. $cot(θ±πn)=cot θ, \period\ π \or\ 180°$
  19. Trigonometric ratio for $(π/2+θ)$ associated angle

  20. $sin(π/2+θ)=cos\ θ$
  21. $cos(π/2+θ)=-sin\ θ$
  22. $tan(π/2+θ)=-cot\ θ$
  23. Trigonometric ratio for $(π±θ)$associated angle

  24. $sin(π±θ)=±sin\ θ$
  25. $cos(π±θ)=-cos\ θ$
  26. $tan(π±θ)=±tan\ θ$
  27. Addition and Subtraction formula

  28. $sin\ (A+B)=sin\ A\ cos\ B+sin\ B\ cos\ A$
  29. $sin\ (A-B)=sin\ A\ cos\ B-sin\ B\ cos\ A$
  30. $cos\ (A+B)=cos\ A\ cos\ B-sin\ A\ sin\ B$
  31. $cos\ (A-B)=cos\ A\ cos\ B+sin\ A\ sin\ B$
  32. $tan\ (A+B)={tan\ A+tan\ B}/{1-tan\ A\ tan\ B}$
  33. $tan\ (A-B)={tan\ A-tan\ B}/{1+tan\ A\ tan\ B$
  34. $cot\ (A+B)={1-tan\ A\ tan\ B}/{tan\ A+tan\ B$
  35. $cot\ (A-B)={1+tan\ A\ tan\ B}/{tan\ A-tan\ B}$
  36. Sum and Product Formula

  37. $sinA+sinB=2sin{A+B}/2cos{A-B}/2$
  38. $sinA-sinB=2cos{A+B}/2sin{A-B}/2$
  39. $cosA+cosB=2cos{A+B}/2cos{A-B}/2$
  40. $cosA-cosB=-2sin{A+B}/2sin{A-B}/2$
  41. $sinA\ sinB=1/2\{cos(A-B)-cos(A+B)\}$
  42. $cosA\ cosB=1/2\{cos(A-B)+cos(A+B)\}$
  43. $sinA\ cosB=1/2\{sin(A+B)+sin(A-B)\}$
  44. $cosA\ sinB=1/2\{sin(A+B)-sin(A-B)\}$
  45. Double Angle Formula

  46. $sin\ 2A=2sinA\ cosA={2tanA}/{1+tan^2A}$
  47. $cos\ 2A=cos^2A-sin^2A=1-2sin^2A$
    $=2cos^2A-1={1-tan^2A}/{1+tan^2A}$
  48. $tan\ 2A={2tanA}/{1-tan^2A}=2/{cotA-tanA}$
  49. Triple Angle Formula

  50. $sin\ 3A=3sinA-4sin^3A=3cos^2A\ sinA-sin^3A$
  51. $cos\ 3A=4cos^3A-3cosA=cos^3A-3cosA\ sin^2A$
  52. $tan\ 3A={3tanA-tan^3A}/{1-3tan^2A}$

Post Tags: HSC | Trigonometry


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