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TI-84 Plus CE field manual for IB Math

AI HL only · 39 of 45

39

Sinusoidal regression

AI HL

Enter periodic paired data, run sinusoidal regression, and read the fitted model y=asin(bx+c)+d.

Goal

Fit a sinusoidal model to ​(0,4.1),  ​(1,5.9),  ​(2,6.3),  ​(3,5.1),  ​(4,2.8),  ​(5,1.7),  ​(6,2.1),  ​(7,3.9), where ​x​ is in radians.

1

Sinusoidal regression only works in radians, so press and make sure RADIAN is selected.

2

Open the list editor with → 1: Edit. Enter the x-values in L1 and the y-values in L2.

NORMALFLOATAUTOREALRADIANMP
L1L2L3L4L504.1------------------15.926.335.142.851.762.173.9------------
3

Run sinusoidal regression: press , move right to CALC, then press for C:SinReg (or scroll down to it and press ). Set Xlist = L1 (type L1 with ) and Ylist = L2 (type L2 with ), then choose Calculate.

Result

The TI-84 uses the form ​y=asin(bx+c)+d, so to three significant figures the model is ​y=2.41sin(0.888x+0.0435)+3.98.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Fit a sinusoidal model ​y=asin(bx+c)+d​ to ​(0,7.5),  ​(1,8.8),  ​(2,8.7),  ​(3,6.6),  ​(4,4.5),  ​(5,2.9),  ​(6,3.4),  ​(7,5.6), where ​x​ is in radians.

  2. 2

    Fit a sinusoidal model to ​(0,3.1),  ​(1,4.6),  ​(2,4.3),  ​(3,2.1),  ​(4,1.3),  ​(5,2.4),  ​(6,4.5),  ​(7,4.4), where ​x​ is in radians.

  3. 3

    Fit a sinusoidal model to ​(0,9.2),  ​(1,12.4),  ​(2,12.3),  ​(3,8.5),  ​(4,5.1),  ​(5,6.3),  ​(6,10.1),  ​(7,13.1), where ​x​ is in radians.