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edenzno
edenzno asked in Science & MathematicsMathematics · 5 years ago

Solving a Trig Equation?

find all solutions on [0, 2pi]

cos(2theta) = -1/2

the olution set is pi/3, 2pi/3, 4pi/3, 5pi/3

I can get pi/3 and 2pi/3, but I don't understand how you can get 4pi/3 and 5pi/3.

Update:

cos(2theta) = -1/2

2 Answers

Relevance
  • ?
    5 years ago

    Because the function corresponding is cos (2 tetha).

    So if tetha is pi/3, by adding pi to tetha, you get 2pi in the function, which is 360 degrees. A circle is 360 degrees and anything pass that is just passing the initial point.

    Any cosine or sines or tangent of an angle added by 360 degrees or 2pi equals the cosine or sine or tangent of the angle itself.

    Cos(x) = Cos (x+2pi)

    Sin(x) = sin (x+2pi)

  • ted s
    Lv 7
    5 years ago

    cos 2Θ = - 1 / 2 ===> 2Θ = either 2π / 3 +2nπ OR 4π / 3 + 2nπ ====> Θ = π / 3 + nπ OR 2π / 3 + nπ ====> π / 3 ; 4 π / 3 OR 2π / 3 ; 5π / 3

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