Express cos4θ and sin4θ in terms of sines and cosines of multiples of θ

Discussion in 'Calculator Requests' started by math_celebrity, Apr 3, 2019.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    Express cos4θ and sin4θ in terms of sines and cosines of multiples of θ.

    Using a trignometric identity:
    cos (2θ) = cos^2(θ) - sin^2(θ)

    Since 4θ = 2*2θ, so we have:
    cos(4θ) = cos^2(2θ) - sin^2(2θ)

    Using another trignometric identity, we have:
    sin(2θ) = 2 sin(θ) cos(θ)

    Since 4θ = 2*2θ, so we have:
    sin(4θ) = 2 sin(2θ) cos(2θ)
     

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