trigonometry

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3. write tan (π/4-β) as a function of β only.

8. write cos(λ+ π/3) as a function of λ only.


16. Write cos(–83°) as a function of a positive angle.

23. Write sin(125°) in terms of its cofunction. Make sure your answer is a function of a positive angle.

31. Find the exact value of sin(195°).

  • trigonometry -

    3.
    tan (π/4-β) = (tanπ/4 - tanβ)/(1+tanπ/4 * tanβ) = (1-tanβ)/(1+tanβ)

    8.
    cos(λ+ π/3) = cosλ cosπ/3 - sinλ sinπ/3
    = 1/2 cosλ - √3/2 sinλ

    16.
    Since cos(-x) = cos(x),
    cos(-83°) = cos(83°)

    23.
    sin(x) = cos(90°-x), so
    sin(125°) = cos(90°-125°) = cos(-35°) = cos(35°)

    31.
    sin(195°) = sin(180°+15°) = -sin(15°) = -sin(30°/2)
    = -√((1-cos(30°))/2)
    = -√(1-√3/2)/2)
    = -√(2-√3) / 2 = -(√3-1) / 2√2

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