Write the equation of a sine function in θ that has amplitude 1/3, period π/4, and phase shift -π/3.

Answer 1

Hello Jada,

You use the general formula f(x) = A*sin(B (x - C) ) + D and apply it to this specific problem.

A represents the amplitude so A = 1/3

B = 2π/period; period = π/4 so B = 2π/(π/4) = 8

C represents the phase shift so C = -π/3

D represents the vertical shift. No vertical shift in the problem you've been given, so D = 0

Plug A, B and C in the general formula ----> f(x) = (1/3)*sin(8(x + π/3))

You can expand the part in bold if you'd like, and you get: f(x) = (1/3)*sin(8x + 8π/3)