pre-calculus help:((((((((

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how do u find period, all angles and name 8 angles for these????????
1)cosxcos2x+sinxsin2x=sqrt(2)/2
2)5cosxsinx+2cosx=0

  • pre-calculus help:(((((((( -

    You have to know your expansion formulas
    to recognize that
    cosx cos2x + sinx sin2x = cos(x-2x)
    = cos(-x)
    but cos(-x) = cos(x)
    so,
    cosx = √2/2
    x = 45° or 315°
    in radians: x = π/4 or 7π/4
    since the original = cosx, and the period of cosx = 360°, the period of the original is 360°
    so add/subtract 360° to any answer to yield more answers until you have 8 of them
    e.g. 45+360 = 405 , another answer

    5cosxsinx + 2cosx=0
    cosx(5sinx + 2) = 0
    cosx = 0 or sinx = -2/5

    if cosx =0, then x = 90° or 270°
    if cosx = -2/5, x = appr. 113.6° or 246.4°
    period again is 360° , etc

    (it asked for all angles, no such thing there would be an infinite number of angles as solutions)

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