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Solve the following equations giving any roots in terms of pi in the .......?
interval -2pi ≤ 0 ≤ 2pi.

a) 2cos²Θ + sin²Θ = 0

b) 2cos²Θ + sin²Θ = 1

c) 2cos²Θ + sin²Θ = 2

  • math -

    First convert cos^2 theta to 1 - sin^2 theta. Then treat sin^2 as a new variable x and solve for that using quadratic equation procedures.

  • math -

    I will do the last one for you

    2cos²Θ + sin²Θ = 2
    2cos²Θ + 1 - cos²Θ = 2
    cos²Θ = 1
    cosΘ = ±1


    in degrees, Θ = 0º or 180º or 360º
    in radians: Θ = 0 pi or 2pi

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