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5 cards from this section. Quick, good the night before a test.
State the amplitude and period of y = 4 sin(3x).
The outside number gives the amplitude; divide 360° by the inside number for the period.
State the maximum and minimum values of y = 3 cos(2x).
Cosine ranges from −1 to 1 before it is multiplied by 3.
What is the amplitude of y = 3 cos(2x)?
Amplitude is measured from the principal axis to a maximum.
What is the period of y = 3 cos(2x)?
Divide 360° by the number multiplying x.
Find the key points of one cycle of y = −2 sin(3x), starting at x = 0°, and describe its shape.
Find the period first, then split it into quarters.
The depth of water in a harbour is modelled by d = 3 cos(30t) + 5, where d is in metres, t is the time in hours after midnight and the angle is in degrees. Find the period, the greatest and least depths, and the first time after midnight when the depth is 6.5 m.
Use the same rules for amplitude, period and principal axis, then solve a simple cosine equation.
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