trigonometry
posted by yoshi on .
3. write tan (π/4β) 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/4β) = (tanπ/4  tanβ)/(1+tanπ/4 * tanβ) = (1tanβ)/(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)
= √((1cos(30°))/2)
= √(1√3/2)/2)
= √(2√3) / 2 = (√31) / 2√2