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virtus

  • 4 years ago

express sin 3theta in terms of sin theta

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  1. Zed
    • 4 years ago
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    http://en.wikipedia.org/wiki/List_of_trigonometric_identities

  2. Zed
    • 4 years ago
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    It's located under Double-, triple-, and half-angle formulae

  3. malevolence19
    • 4 years ago
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    \[\sin(3 \phi)=\frac{e^{3i \phi}-e^{-3i \phi}}{2i}\] Then use: \[e^{3i \phi}=(e^{i \phi})^3; e^{i \phi}=\cos(\phi)+i \sin(\phi)\] Then set the real part equal.

  4. virtus
    • 4 years ago
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    thanks but i do not really understand the working out

  5. rivermaker
    • 4 years ago
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    If you know the formula for \[\sin (A+B)\] then you can derive the formula for \[\sin 2A = \sin (A + A)\] and \[\sin 3A = \sin (A + 2A) \]

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