Problem preview
F-TF.5 Warmup M3-036-A11-V01

Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.

Compare sinusoidal models with parallel feature fields

Problem

Compare \(A(x)~=~2\sin(x)~+~5\) and \(B(x)~=~3\sin(x)~+~5\). Use the graph to state each amplitude, period, midline, and range, then describe their shared features and differences.

Big Picture

What this problem is really about

Compare sinusoidal models one feature field at a time. Outside coefficients control vertical scale, outside constants control the common centerline, and inside coefficients and shifts control cycle length and phase. After finding each range from midline plus or minus amplitude, use aligned crossings and extrema to confirm which timing features are shared and which vertical features differ.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
F-TF.5
Category
Functions
Domain
Trigonometric Functions
Objective
Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Problem type
Compare sinusoidal models with parallel feature fields