Sinusoidal models describe quantities that repeat in regular intervals, or periodically, and are of the form y=asin(bx)+c or y=acos(bx)+c.
A sinusoidal curve y=acos(bx)+c is graphed below with key features.
The principal axis, the line around which the sinusoid oscillates, is given by y=c.
The amplitude, or the maximum distance the sinusoid reaches above and below the principal axis, is a.
The period, or the horizontal distance between consecutive maxima, is given by b360° (or b2πrad for HL).
If a sinusoidal model has a phase shift, it has been moved horizontally. Now, f(x)=asin(b(x−h))+c, where h is the phase shift.
Your calculator should have a function called sinusoidal regression which you can use when you know at least 4 points on a sinusoidal function, and you can estimate the period. To use it, first enter the x coordinates (or independent variables) into L1 and the y coordinates (or dependent variable) into L2.
The calculator will likely ask you to provide a number for "iterations", which is simply the number of "loops" it makes in refining its approximation. 5 will be plenty unless a problem asks for a very high degree of accuracy.
Nice work completing Sinuisoidal Models, here's a quick recap of what we covered:
Exercises checked off
Sinusoidal models describe quantities that repeat in regular intervals, or periodically, and are of the form y=asin(bx)+c or y=acos(bx)+c.
A sinusoidal curve y=acos(bx)+c is graphed below with key features.
The principal axis, the line around which the sinusoid oscillates, is given by y=c.
The amplitude, or the maximum distance the sinusoid reaches above and below the principal axis, is a.
The period, or the horizontal distance between consecutive maxima, is given by b360° (or b2πrad for HL).
If a sinusoidal model has a phase shift, it has been moved horizontally. Now, f(x)=asin(b(x−h))+c, where h is the phase shift.
Your calculator should have a function called sinusoidal regression which you can use when you know at least 4 points on a sinusoidal function, and you can estimate the period. To use it, first enter the x coordinates (or independent variables) into L1 and the y coordinates (or dependent variable) into L2.
The calculator will likely ask you to provide a number for "iterations", which is simply the number of "loops" it makes in refining its approximation. 5 will be plenty unless a problem asks for a very high degree of accuracy.
Nice work completing Sinuisoidal Models, here's a quick recap of what we covered:
Exercises checked off