what is the solution set to cos2x=0?

thanks

2 Answers

  • Cos(2x) = 2cos²(x) -1 So substituting this we get

    2cos² (x) – 1 =0

    Now solve as a regular equation, add 1, divide by 2, take the square root

    2cos² (x)= 1

    cos²(x)=1/2

    cos(x)= +/- √2/2

    So at what angle does cosine (x-value) equal -√2/2 and positive √2/2?

    45 degrees, 135, 225, 315 or use the ratio (180/pi) to convert to radian pi/4, 3pi/4, 5pi/4, 7pi/4

    Alternatively, you could have replaced 2x with Θ to get

    cos(Θ)=0

    Think where does theta equal 0, that would be at Θ=pi/2 + 2(pi)(k) and Θ=3pi/2 + 2(pi)(k) where k is a positive integer

    Next replace Θ with 2x

    2x=pi/2 + 2(pi)k

    Solve for x to get

    x=pi/4 + pi(k)

    x=3pi/4 + pi(k)

    Then just plug in for k

    When k=0, x= pi/4, 3pi/4

    k=1 x = 5pi/4, 7pi/4 and so on

  • In radians: cos (2x) = 0 –> 2x = pi/2, 3pi/2, …. so x = pi/4, 3pi/4, …

    In degrees cos(2x) = 0 –> 2x = 90, 270, 450, … so x = 45, 135, 225,…

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