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Find all the values of x between 0 and 2(pi) for which
sin x + (root 3)cos x = 0

  • Maths -

    Whenever you see sines and cosines and sqrt 3, draw a thirty, sixty ninety triangle.
    the sin of the 60 degree angle is (sqrt 3)/2
    the cosine of the 60 degree angle is 1/2
    sqrt(3)/2 = (sqrt 3)(1/2)
    Now the quadrants where the sine and cosine have opposite signs are quadrant 2 and quadrant four. So look in those two quadrants.

  • Maths -

    another not necessarily better approach would be ...

    sinx = -√3cosx
    tanx = -√3

    from the same triangle as Damon's we would get a "basic" angle of 60ยบ or pi/3 radians

    but the tan is negative in II or IV, so
    x = pi - pi/3 or 2pi - pi/3
    or x = 2pi/3 or 5pi/3

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