CCSS HSF-TF.B.5 Worksheets
Algebra 2 · Trigonometric Functions
Choose sine and cosine functions to model periodic phenomena with a specified amplitude, period (frequency) and midline, and identify the amplitude, period, phase shift and midline of a given sinusoid.
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Teaching guide
What students learn
Choose sine and cosine functions to model periodic phenomena with a specified amplitude, period (frequency) and midline, and identify the amplitude, period, phase shift and midline of a given sinusoid.
Worked example
For y = -2sin(3(x + π/2)) + 1, state the amplitude, period, phase shift and midline.
Answer: Amplitude 2; period 2π/3; phase shift -π/2 (left); midline y = 1
Why: Amplitude = |a| = |-2| = 2. Period = 2π/|b| = 2π/3 = 2π/3. Phase shift = -π/2 (left). Vertical shift d = 1, so the midline is y = 1. The negative amplitude reflects the curve across its midline.
Generated and checked in code, so it is correct.
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