Evaluate the following .?

Update:

Edit : Plz Read the numerator as 4 ( cos 75 + i sin 75 )

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  • 7 months ago
    Favorite Answer

    It's a simple question. You have to use simple formulae -

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  • sepia
    Lv 7
    7 months ago

    (4 cos 75° + i sin 75°) / (4(cos 30° + i sin 30°))

    = (0.3449 + 0.07972 i)

  • 7 months ago

    360 = 2*2*2*3*3*5 and 75 = 3*5*5

    The LCM of 75 and 360 = 5*360 = 1800.

    Note 5*360=1800 and 24*75 = 1800.

    1800º = 5*360º = 10π rad.  And since 1800/75 = 24:

    75º = (10π)/24 = (5/12)π rad.

    cos(75º) + isin(75º) =  (cos((5/12)π) + isin((5/12)π)

    . . . . . . . . . . . . . . . .= e^((5/12)πi)

    ____________

    Since 30º =  π/6 rad:

    cos(30º) + isin(30º) = cos((π/6)i) + isin((π/6)i)

    . . . . . . . . . . . . . . . . = e^((π/6)i)

    ____________

    So your expression becomes:

    4e^((5/12)πi)  / (0.4 e^((π/6)i)))

    = 10 e^((3/12)πi (since e^x/e^y = e^(x-y) and 5/12-1/6 = 3/12)

    = 10 e^(π/4)i)’

    Since π/4 =45º you could write this as:

    10(cos(45º) + isin(45º))

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