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ajprincess Group Title

Note to the viewers:This is not a question but short notes on trigonometric identities that may be of some use.

  • 2 years ago
  • 2 years ago

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  1. ajprincess Group Title
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    |dw:1339728896748:dw| a-opposite b-adjacent c-hypotenuse. \[\sin \theta=a/c\] \[\cos \theta=b/c\] \[\tan \theta=a/b\] \[\csc \theta=1/\sin \theta=1/a/c=c/a\] \[\sec \theta=1/\cos \theta=1/b/c=c/b\] \[\cot \theta=1/\tan \theta=1/a/b=b/a\] \[\sin ^{2}\theta+ \cos ^{2}\theta=1\] \[\tan ^{2}\theta+1=\sec ^{2}\theta\] \[1+\cot^{2}\theta=\csc^{2}\theta\] \[tan\theta*\cot\theta=1\] \[sin(A+B)=sinAcosB+sinBcosA\] \[cos(A+B)=cosAcosB+sinAsinB\] \[tan(A+B)=(tanA+tanB)/(1-tanA*tanB)\] \[sin(A-B)=sinAcosB-sinBcosA\] \[cos(A-B)=cosAcosB-sinAsinB\] \[tan(A-B)=(tanA-tanB)/(1+tanA*tanB)\]

    • 2 years ago
  2. ajprincess Group Title
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    \[sin(A+B)+sin(A-B)=2sinAcosB\] \[cos(A+B)+cos(A-B)=2cosAcosB\] \[sin(A+B)-sin(A-B)=2cosAsinB\] \[cos(A-B)-cos(A+B)=2sinAsinB\] \[sin2\theta=2sin\theta\cos\theta\] \[cos2\theta=cos^2\theta-sin^2\theta\] \[cos2\theta=1-2sin^2\theta\] \[cos2\theta=2cos^2\theta-1\] \[tan2\theta=2tan\theta/(1-tan^2\theta)\] \[sin3\theta=3sin\theta-4sin^3\theta\] \[cos3\theta=4cos^3\theta-3cos\theta\] \[sin(-\theta)=-sin\theta\] \[cos(-\theta)=cos\theta\] \[tan(-theta)=-tan\theta\]

    • 2 years ago
  3. ajprincess Group Title
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    \[sin(90-\theta)=cos\theta\] \[cos(90-\theta)=sin\theta\] \[tan(90-\theta)=cot\theta\] \[sin(180-\theta)=sin\theta\] \[cos(180-\theta)=-cos\theta\] \[tan(180-\theta)=-tan\theta\] \[sin(180+\theta)=-sin\theta\] \[cos(180+\theta)=-cos\theta\] \[tan180+\theta)=tan\theta\] \[sin(90+\theta)=cos\theta\] \[cos(90+\theta)=-sin\theta\] \[tan(90+\theta)=-cot\theta\]

    • 2 years ago
  4. ajprincess Group Title
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    • 2 years ago
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  5. maheshmeghwal9 Group Title
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    Nice & thanx @ajprincess :)

    • 2 years ago
  6. ajprincess Group Title
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    U r welcome nd thanxx. I thank all who gav me medals for givng them.:)

    • 2 years ago
  7. alexwee123 Group Title
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    nice :)

    • 2 years ago
  8. maheshmeghwal9 Group Title
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    very nice:)

    • 2 years ago
  9. ajprincess Group Title
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    Thanxxx a lot for the comments.:)

    • 2 years ago
  10. experimentX Group Title
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    seems like you used in few ,,,

    • 2 years ago
  11. lgbasallote Group Title
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    this is a true tutorial indeed \[\Huge \color{maroon}{\mathtt{\text{<tips hat>}}}\]

    • 2 years ago
  12. ajprincess Group Title
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    Thanx a lot @lgbasallote

    • 2 years ago
  13. WONDEMU Group Title
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    how should I memorize these?

    • 2 years ago
  14. Loujoelou Group Title
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    I liked it :) Good Job making it :)

    • 2 years ago
  15. ajprincess Group Title
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    Thanx a lot @Loujoelou and as for question @wondemu memorise them group by group. For example (1)sin(A+B)=sinAcosB+sinBcosA cos(A+B)=cosAcosB+sinAsinB tan(A+B)=(tanA+tanB)/(1−tanA∗tanB) (2)sin(A−B)=sinAcosB−sinBcosA cos(A−B)=cosAcosB−sinAsinB tan(A−B)=(tanA−tanB)/(1+tanA∗tanB) You'll find them useful when u hav finishd memorising them.

    • 2 years ago
  16. apoorvk Group Title
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    Simple, clear, lucid, and great! :P

    • 2 years ago
  17. ajprincess Group Title
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    Thanx a lot @apoorvk

    • 2 years ago
  18. maheshmeghwal9 Group Title
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    Wow reaching the same target as lgba {30 medals} But hope u would get more than that ^_^

    • 2 years ago
  19. ajprincess Group Title
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    Thanx a lot @maheshmeghwal9

    • 2 years ago
  20. maheshmeghwal9 Group Title
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    :)

    • 2 years ago
  21. mathslover Group Title
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    good tutorial must appreciate ...

    • 2 years ago
  22. ajprincess Group Title
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    Thanx a lot @mathslover.

    • 2 years ago
  23. mathslover Group Title
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    no thanks @ajprincess actually many of students present here needed this

    • 2 years ago
  24. ajprincess Group Title
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    :)

    • 2 years ago
  25. Calcmathlete Group Title
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    Good job :) I actually didn't know the negative and triple identities.

    • 2 years ago
  26. ajprincess Group Title
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    thanx a lot @calcmathlete

    • 2 years ago
  27. phani09 Group Title
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    that was a good revision.....

    • 2 years ago
  28. ajprincess Group Title
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    Thanx a lot @phani09

    • 2 years ago
  29. waterineyes Group Title
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    @ajprincess , I want to tell you something if you will not feel bad.. May I tell??

    • 2 years ago
  30. eliassaab Group Title
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    http://www.sosmath.com/trig/Trig5/trig5/trig5.html

    • 2 years ago
  31. ajprincess Group Title
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    ya sure. @waterineyes.

    • 2 years ago
  32. waterineyes Group Title
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    Can you tell me the formulas for \(cos(A + B) \quad and \quad cos(A-B)\) ??

    • 2 years ago
  33. waterineyes Group Title
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    @ajprincess, do you think that you have given the right identities for \(cos(A + B) \quad and \quad cos(A - B)\) ??

    • 2 years ago
  34. Calcmathlete Group Title
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    @waterineyes is correct. Those two identities are incorrect. \[cos(A + B) = \cos A\cos B - \sin A\sin B\]\[cos(A - B) = \cos A\cos B + \sin A\sin B\]

    • 2 years ago
  35. waterineyes Group Title
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    See, the difference between \(sin(A \pm B) \quad And \quad cos(A \pm B)\): \[\Large \color{green}{\sin(A \pm B) = sinA.cosB \pm cosA.sinB}\] \[\Large \color{green}{\cos(A \pm B) = cosA.cosB \mp cosA.cosB}\]

    • 2 years ago
  36. waterineyes Group Title
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    @ajprincess , don't misunderstand me and don't think I always look for mistakes but everywhere you used this identity wrong.. So, I think your mind says it is correct but sorry to say it is incorrect... In sin(A + B) there is respective + in the middle, In sin(A - B) there is respective - in the middle.. But for cos(A + B), there is - in the middle, for cos(A - B), there is + in the middle... Getting it??

    • 2 years ago
  37. ajprincess Group Title
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    oh no it's k. Thanx for telling t. i copied it from a note of mine. i must hav written it wrong when I wrote. thanxx a lot for mentioning it. I welcome this sorts of comments. @waterineyes.

    • 2 years ago
  38. waterineyes Group Title
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    26 people gave you medals and I think you deserve more than that.. But how will you let it know to all the 26 people that you have written slight wrong there so that they can know the real formula... Think about it.. @ajprincess ..

    • 2 years ago
  39. ajprincess Group Title
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    it's my mistake nd I am greatly sorry for t. Let me post t again in a new post so that they can get . I am nt sure of any other way other than this.

    • 2 years ago
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