Pre-Cal

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Find all the soultions of the equation in the interval (0,2pi)

sin 2x = -sqrt3 /2

sin -sqrt3 /2 is 4pi/3 and 5pi/3 in the unit circle

2x= 4pi/3 + 2npi 2x=5pi/3 + 2npi

I do not know what to do at this point.

  • Pre-Cal -

    30, 60, 90 triangle
    1, sqrt 3,sides and 2 hypotenuse

    sin A = + (sqrt 3)/2 if A = pi/3
    so
    if A = pi + pi/3 which is 4 pi/3
    or
    if A = 2 pi - pi/3 which is 5 pi/3

    then sin A = -sqrt(3) /2 {AGREE}
    But A = 2x
    so
    x = 2 pi/3 or 5 pi/6

    Now if they mean x can be as large as 2 pi we better look for bigger angles for A
    Like A = 2 pi + 4 pi/3 = 10 pi/3
    then x = 5 pi/3
    and
    Like A = 2 pi + 5 pi/3 = 11 pi/3
    then x = 11 pi/6
    which is still less than 2 pi (barely
    so
    I get four values for x total

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