trigonometry

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find cos(θ)ˏsin(θ)ˏtan(θ), if cot (2θ)=5/12 with 0≤2θ≤π - -

  • trigonometry -

    If cot(2Ø) = 5/12 , then
    tan(2Ø) = 12/5 and 2Ø is in either I or III

    tan 2Ø = 2tanØ/(1 - tan^2 Ø)
    let tanØ = u
    then 12/5 = 2u/(1 - u^2) , (for easier typing)

    10u = 12 - 12u^2
    12u^2 + 10u - 12 = 0
    6u^2 + 5u - 6 = 0
    (2u + 3)(3u - 2) = 0
    u = -3/2 or u = 2/3
    tanØ = -3/2 or tan u = 2/3

    case 1:
    tanØ = -3/2--> Ø in II or IV
    make a sketch of a right right-angled triangle
    hypotenuse = √(3^2+2^2) = √13
    IN II: sinØ = 2/√13 , cosØ = -3/√13, tanØ = -3/2
    IN IV: sinØ = -2/√13 , cosØ = 3/√13, tanØ = -3/2

    case 2:
    tanØ = 2/3---> Ø in I or III
    make a new sketch, hypotenuse is still √13
    IN I: sinØ = 3/√13, cosØ = 2/√13 , tanØ = 2/3
    IN III: sinØ = -3/√13 , cosØ = -2/√13, tanØ = 2/3


    check my arithmetic, should have written it out on paper first.

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