Hi, I'm in need of some help understanding some of my precalculus homework. Suppose θ is an angle such that cos θ = 3/4. Evaluate cos(2θ).?

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  • 1 month ago

    cos θ = 3/4. 

    cos(2 θ) = cos(2 cos^(-1)(3/4)) = 1/8

  • 1 month ago

    The answer is as follows:

    Attachment image
  • Philip
    Lv 6
    2 months ago

    Replace theta by x.

    cos(x) = (3/4);

    cos(2x) = 2cos^2(x) - 1 = 2(9/16) - 1 = 18/16 -1 = 2/16 = 1/8.

  • ?
    Lv 7
    2 months ago

    cos θ = 3/4

    cos 2θ =  2 cos² θ -1

    ............= 2 (3/4)² - 1

    ............= 2 (9/16) - 1

    ............= 18/32 - 1

    ............= -14/32

    ............= -7/16..............ANS

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  • 2 months ago

    Trig Identity: cos(2x) = 2cos²(x) – 1

    Given: cos(θ) = 3/4

    cos(2θ) = 2cos²(θ) - 1

    cos(2θ) = 2(3/4)² - 1

    cos(2θ) = 2(9/16) - 1

    cos(2θ) = 1/8

  • 2 months ago

    ACOS(3/4) = 41.4126724 deg so that 2theta = 82.82 and cos(82.82) = 0.124986913  ANS.

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