Unit 5 · Core unit
Four parameters that describe any sinusoid, and using them to model anything that repeats.
What a strong answer looks like
A strong answer factors the inside coefficient out before reading a phase shift, and interprets midline and amplitude in context.
Know
Amplitude is the absolute value of the front coefficient, period is a full turn divided by the inside coefficient, and the trailing constant sets the midline.
Apply
Read amplitude and midline directly; compute the period.
Watch out
Treating the inside coefficient as the period rather than dividing into a full turn.
Study move
State all four parameters for a given sinusoid and check against a graph.
Know
A phase shift is only visible after the inside coefficient is factored out of the argument.
Apply
Rewrite the argument in factored form, then read the shift.
Watch out
Reading the shift straight from the unfactored constant, which every distractor set exploits.
Study move
Factor an argument and state the actual shift.
Know
Midline and amplitude come from the extremes; period comes from how often the pattern repeats; the starting position chooses the function and its sign.
Apply
Decide where the phenomenon starts before choosing sine or cosine.
Watch out
A model with correct parameters that starts at a maximum when the situation starts at a minimum.
Study move
Model a tide from its extremes and cycle length, then verify at time zero.
Modeling drill
A depth varies between 3 and 11 metres every 12 hours, starting at its lowest. Build the model and check it at time zero.
