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M3-036-A09-V02
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F-TF.5
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M3-036-A09-V02
Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Find and verify sinusoidal maximum and minimum values
Problem
For \(h(t)~=~12~-~5\cos(t)\), use the envelope diagram to state the amplitude, midline, maximum, minimum, and range, then verify the midpoint and half-range relationships.
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A
The amplitude is 5, the midline is 12, the maximum is 22, the minimum is 2, and the range is [2, 22]. The midpoint check is (maximum + minimum)/2 = 12, and the half-range check is (maximum - minimum)/2 = 10.
B
The amplitude is -5, the midline is 12, the maximum is 7, the minimum is 17, and the range is [17, 7]. The midpoint check is (maximum + minimum)/2 = 12, and the half-range check is (maximum - minimum)/2 = -5.
C
The amplitude is 5, the midline is 12, the maximum is 7, the minimum is 17, and the range is [17, 7]. The midpoint check is (maximum + minimum)/2 = 12, and the half-range check is (maximum - minimum)/2 = -5.
D
The amplitude is 5, the midline is 12, the maximum is 17, the minimum is 7, and the range is [7, 17]. The midpoint check is (maximum + minimum)/2 = 12, and the half-range check is (maximum - minimum)/2 = 5.
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Curriculum context
Standard F-TF.5
Category Functions
Domain Trigonometric Functions
Objective Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Problem type Find and verify sinusoidal maximum and minimum values
