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saifoo.khan Group Title

Easy trig problem below:

  • 2 years ago
  • 2 years ago

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  1. jasonxx Group Title
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    ?

    • 2 years ago
  2. saifoo.khan Group Title
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    \[\frac{3A}{sinA} + \frac{\cos3A}{\cos A}≡ 4 \cos 2A\]

    • 2 years ago
  3. jasonxx Group Title
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    cos(3A) = cos(2A+A) =4 cos³ A - 3 cos A

    • 2 years ago
  4. jasonxx Group Title
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    taking the LCM and then using 2 sinA * cos A= sin 2A

    • 2 years ago
  5. jasonxx Group Title
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    and cos 2A= cos^2 2A -1

    • 2 years ago
  6. saifoo.khan Group Title
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    I'm not sure about your working but i completed till here: \[\frac{\cos A \sin 3A + \cos 3A \sin A}{\sin A \cos A}\]

    • 2 years ago
  7. saifoo.khan Group Title
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    Then: \[\frac{\sin(A+3A)}{\sin A \cos A}\]idk what to do after this..

    • 2 years ago
  8. saifoo.khan Group Title
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    @jasonxx ?

    • 2 years ago
  9. jasonxx Group Title
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    well, i guess expand everything

    • 2 years ago
  10. zepdrix Group Title
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    \[\frac{\sin(4A)}{\frac{1}{2}\sin(2A)}\] This the next step? :) hmm fun problem.

    • 2 years ago
  11. zepdrix Group Title
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    \[\frac{4\sin(2A) \cos(2A)}{\sin(2A)}\] \[=4\cos(2A)\] Something like that... :D Yayyy team!

    • 2 years ago
  12. saifoo.khan Group Title
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    HOW? HOW? HOW?

    • 2 years ago
  13. jasonxx Group Title
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    sin(4A)=sin(2* 2A)

    • 2 years ago
  14. zepdrix Group Title
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    Oh like say what each step that's being performed? :D

    • 2 years ago
  15. saifoo.khan Group Title
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    Last 3 steps, yes sir. @zepdrix ;D

    • 2 years ago
  16. jasonxx Group Title
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    and sin (2*2A) is like sin (2* X)= 2*2 sin (2A)cos(2A)

    • 2 years ago
  17. zepdrix Group Title
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    Hmm so we're taking advantage of Sine's Double Angle Formula, On top, in one direction, on the bottom in the other direction. Yah looks like Jason has the right idea also ^^

    • 2 years ago
  18. jasonxx Group Title
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    :)) thanks @zepdrix

    • 2 years ago
  19. saifoo.khan Group Title
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    I have this general formula with me: sin2A = 2sinAcosA But how did you guys converted sin4A into this?

    • 2 years ago
  20. jasonxx Group Title
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    Let's say A=X then its gona be sin (2X), now X=2A therefore its gona be the conversion mentioned above

    • 2 years ago
  21. saifoo.khan Group Title
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    I think i got it now. Thanks @jasonxx and @zepdrix . :)

    • 2 years ago
  22. jasonxx Group Title
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    :) keep rockin

    • 2 years ago
  23. zepdrix Group Title
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    Oh sorry. I wasn't going into much detail because I thought you were testing us :) lol

    • 2 years ago
  24. saifoo.khan Group Title
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    Lol. No. this was the last problem of 26. i had the answers but wasn't getting the last step!

    • 2 years ago
  25. saifoo.khan Group Title
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    @zepdrix Where did the 1/2 in your second last step go? D:

    • 2 years ago
  26. zepdrix Group Title
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    So we're dividing by a fraction, let's fix that a sec. \[\frac{\sin(4A)}{\frac{1}{2}\sin(2A)} \quad = \quad \frac{2\sin(4A)}{\sin(2A)}\] Then we apply the Sine Double Angle Formula to the top part.\[\frac{2\sin(2\cdot 2A)}{\sin(2A)} \quad = \quad \frac{2\cdot 2 \sin(2A)\cos(2A)}{\sin(2A)}\]

    • 2 years ago
  27. saifoo.khan Group Title
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    Oh! Now it makes perfect sense to me!

    • 2 years ago
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