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°).
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