Math Problem Statement

Use a graphing calculator to find the sine function that best fits the data. y ( t )

t y 0.01 11.6 0.02 15.69 0.03 18.72 0.04 19.9 0.05 18.93 0.06 16.06 0.07 12.03 0.08 7.89 0.09 4.71 0.1 3.32 0.11 4.08 0.12 6.79 0.13 10.75 0.14 14.92 0.15 18.24

Comments: Enter your answer as an expression, and be sure your variables match those in the question. Enter at least 2 decimal places for each value from the calculator (and remember to round appropriately).

Solution

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sine Functions
Data Fitting
Regression Analysis

Formulas

y(t) = a sin(b t + c) + d
Amplitude: a = (max(y) - min(y)) / 2
Vertical Shift: d = (max(y) + min(y)) / 2
Angular Frequency: b = 2π / T

Theorems

Periodicity of Sine Functions
Regression Analysis

Suitable Grade Level

Grades 11-12