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Determine the roots of the function f(x)=-2cos(3x)-1. Can you please show all the work so it is easier to understand, thank you!!

  • Trig -

    set 2cos(3x) - 1 = 0
    2cos(3x) = 1
    cos 3x = 1/2
    I will use degrees, we can always switch to radians later
    3x = 60° or 3x = 300° by the CAST rule
    x = 20° or x = 100°

    the period of cos 3x = 360/3 or 120°
    so by adding/subtracting 120° to any of our answers we can produce as many new answers as we want,
    so for 0 ≤ x ≤ 360°
    x = 20°, 140°,100° , 220° , 260°, 340°

    or in radians
    x = π/9, 7π/9, 5π/9, 11π/9 , 13π/9, 17π/9

  • Trig -

    Ok so how did you get x to equal 20, 140,100........
    And I also don't get where 3x=60 or 100 came from, can you please explain these parts by showing the math? Thank you

  • Trig -

    I knew, or my calculator told me, that
    cos 60° = 1/2 or cos 300° = 1/2
    so 3x had to be 60° or 3x had to be 300°

    well if 3x = 60 , what is x? (divide both sides by 3)
    same for 3x = 300
    x = 100

    (on your calc.

    you should get 60 )

  • Trig -

    Srry I keep asking questions, but I noticed that you left out the negative sign on the 2 when you set the equation to zero, was that a mistake or were you suppose to do it like that?

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