Sinusoidal Modeling (Set Calculators to DEGREE mode)

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Presentation transcript:

Sinusoidal Modeling (Set Calculators to DEGREE mode)

Transformations of Sinusoidal Functions Amplitude |a|: a controls vertical stretching/shrinking Period p can be in radians or degrees: p is the horizontal length to complete one cycle Horizontal shift b can be in radians or degrees: b controls horizontal stretching/shrinking Vertical shift d: +d , shift d units up –d , shift d units down Horizontal phase shift c (proportionally scaled to 2 radians or 360): –c, shift c units right +c, shift c units left where, xstart corresponds with the first point of the sine or cosine cycle

Annual Temperature Change (MD) Amplitude (a) Period (p) b Vertical Shift (d) Phase Shift (c), for Sine c= –120, since shift RIGHT Annual Temperature Change (MD) Sine Model Phase Shift (c), for Cosine Cosine Model c= –210, since shift RIGHT

Annual Temperature Change (MD) Amplitude (a) Period (p) b Vertical Shift (d) Phase Shift (c), for Sine Annual Temperature Change (MD)

Annual Temperature Change (MO) Amplitude (a) Period (p) b Vertical Shift (d) Phase Shift (c), for Sine c= –120, since shift RIGHT Annual Temperature Change (MO) Sine Model Phase Shift (h), for Cosine Cosine Model c= –210, since shift RIGHT

Annual Temperature Change (MO) Amplitude (a) Period (p) b Vertical Shift (d) Phase Shift (c), for Sine Annual Temperature Change (MO)

Sine Model Tide Height Cosine Model Amplitude (a) Period (p) b Vertical Shift (d) Phase Shift (c), for Sine c= -150, since shift RIGHT Sine Model Tide Height Phase Shift (h), for Cosine Cosine Model c= –60, since shift RIGHT

Tide Height Amplitude (a) Period (p) b Vertical Shift (d) Phase Shift (c), for Sine Tide Height

Sine Model Predator/Prey Cosine Model Amplitude (a) Period (p) b Vertical Shift (d) Phase Shift (c), for Sine Sine Model Predator/Prey Phase Shift (h), for Cosine Cosine Model h= –90, since shift RIGHT

Predator/Prey Amplitude (a) Period (p) b Vertical Shift (d) Phase Shift (c), for Sine Predator/Prey