trigonometry

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°).

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1. 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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posted by Steve

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