AP Precalculus Section 3.7 Example: TI-84+ Calculator to Write a Sinusoidal Equation (SinReg) #1

Random AP Precalculus Problems (I found on the Internet). These are not official AP Collegeboard examples, but they will definitely get the job done!

To use the TI-84+ calculator to write a sinusoidal equation using the SinReg (Sine Regression) function, follow these steps:

1. **Enter Data:**
- Go to the "STAT" menu by pressing the `STAT` key.
- Enter your data into two lists, typically L1 for the x-values and L2 for the y-values.

2. **Turn Diagnostics On (Optional):**
- For a more detailed sinusoidal regression, you can turn on the diagnostics by pressing `2nd` + `0` (CATALOG).
- Scroll down to "DiagnosticOn" and press `ENTER`. Select it and press `ENTER` again.

3. **Access SinReg:**
- Press `STAT` and then go to the "CALC" menu.
- Scroll down to "SinReg" and press `ENTER`.

4. **Specify Lists:**
- A prompt will appear asking for the lists where your x and y data are stored. Enter the lists (e.g., L1, L2) and press `ENTER`.

5. **Store Regression Equation:**
- After pressing `ENTER`, the calculator will display the regression equation in the form \(y = A \sin(Bx + C) + D\).
- The values for \(A\), \(B\), \(C\), and \(D\) are the coefficients of the sinusoidal equation.

6. **Turn Off Diagnostics (Optional):**
- If you turned on diagnostics, you may want to turn it off after obtaining the regression equation. To do this, go to "DiagnosticOn" in the CATALOG, select it, and press `ENTER`.

Now you have the sinusoidal equation based on the SinReg function. The regression equation will allow you to model the data with a sine function. Note that the calculator performs a best-fit regression, and the equation may not precisely match the data points but provides a reasonable sinusoidal model.

The Topics covered in AP Precalculus are...

1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
1.4 Polynomial Functions and Rates of Change
1.5 Polynomial Functions and Complex Zeros
1.6 Polynomial Functions and End Behavior
1.7 Rational Functions and End Behavior
1.8 Rational Functions and Zeros
1.9 Rational Functions and Vertical Asymptotes
1.10 Rational Functions and Holes
1.11 Equivalent Representations of Polynomial and Rational Expressions
1.12 Transformations of Functions
1.13 Function Model Selection and Assumption Articulation
1.14 Function Model Construction and Application
2.1 Change in Arithmetic and Geometric Sequences
2.2 Change in Linear and Exponential Functions
2.3 Exponential Functions
2.4 Exponential Function Manipulation
2.5 Exponential Function Context and Data Modeling
2.6 Competing Function Model Validation
2.7 Composition of Functions
2.8 Inverse Functions
2.9 Logarithmic Expressions
2.10 Inverses of Exponential Functions
2.11 Logarithmic Functions
2.12 Logarithmic Function Manipulation
2.13 Exponential and Logarithmic Equations and Inequalities
2.14 Logarithmic Function Context and Data Modeling
2.15 Semi-log Plots
3.1 Periodic Phenomena
3.2 Sine, Cosine, and Tangent
3.3 Sine and Cosine Function Values
3.4 Sine and Cosine Function Graphs
3.5 Sinusoidal Functions
3.6 Sinusoidal Function Transformations
3.7 Sinusoidal Function Context and Data Modeling
3.8 The Tangent Function
3.9 Inverse Trigonometric Functions
3.10 Trigonometric Equations and Inequalities
3.11 The Secant, Cosecant, and Cotangent Functions
3.12 Equivalent Representations of Trigonometric Functions
3.13 Trigonometry and Polar Coordinates
3.14 Polar Function Graphs
3.15 Rates of Change in Polar Functions

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:

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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

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