A tide is modeled v the duty y=1/2sin(3θ), where θ is in radians. Define the graph the this function, consisting of its period, amplitude, and also points of intersection through the x-axis.

You are watching: A wave is modeled with the function y=1/2 sin 3 theta


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A general sine duty has the form:

y = a·sin(b(θ-c)) + d

a = amplitudeb = angular frequency (radians/sec) = 2π/period.c = step (horizontal) shiftd = vertical shift

You role is:

y = (1/2)·sin(3(θ-0)) + 0 = (1/2)·sin(3θ)

a = amplitude = 1/2b = angular frequency = 3 = 2π/period, so duration = 2π/3c = phase change = 0 (no phase shift)d = vertical change = 0 (no upright shift)

It intersects the x-axis when y = 0

0 = (1/2)·sin(3θ)

which occurs when 3θ = ± n·π, n = 0, 1, 2, 3, 4, ..., or θ = ± n·π/3, n = 0, 1, 2, 3, 4,


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