AP Precalculus Section 3.10 Example:TI-84+ Calculator (Sinusoidal Word Problem about Maximums)

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 find the maximum of a sinusoidal function, you can follow these steps:

1. **Enter the Sinusoidal Function:**
- Press the `Y=` key to enter the equation editor.
- Enter the sinusoidal function in terms of \(x\), using the appropriate variables for amplitude (\(A\)), frequency (\(B\) for period), phase shift (\(C\)), and vertical shift (\(D\)).
- For example, if your function is \(y = A \sin(Bx + C) + D\), input the corresponding values for \(A\), \(B\), \(C\), and \(D\).

2. **Adjust the Window:**
- Press the `WINDOW` key to set the window parameters. Make sure the X-axis range includes the values relevant to the problem.
- Set the Y-axis range to include the expected range of function values.

3. **Graph the Function:**
- Press the `GRAPH` key to visualize the graph of the sinusoidal function.
- Look for the highest point on the graph, which corresponds to the maximum value.

4. **Use the Trace Function:**
- Press the `TRACE` key to use the trace function.
- Move the cursor along the graph by pressing the right arrow key until you reach the peak of the sinusoidal function.
- The maximum value of the function will be displayed on the screen.

5. **Read the Maximum Value:**
- The maximum value will be displayed on the screen when the cursor is at the peak of the graph.
- Take note of the \(x\)-coordinate and \(y\)-coordinate of the maximum point.

6. **Alternatively, Use the Calculate Menu:**
- Press the `2ND` key and then the `CALC` key to access the calculate menu.
- Select option `4: maximum` and press enter.
- Follow the on-screen instructions to input the left bound, right bound, and guess for the maximum. The calculator will then calculate and display the maximum value.

7. **Verify the Results:**
- Check the calculated maximum value by comparing it to the graph. Ensure that it aligns with the highest point on the graph.

By following these steps, you can use your TI-84+ calculator to find the maximum value of a sinusoidal function graphically or by using the calculate menu. Remember to adjust the window settings appropriately to visualize the relevant portion of the graph.

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:

/ nickperich

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

#APPrecalculus
#PreCalcProblems
#MathMinds
#AdvancedPreCalc
#TrigTales
#PrecalcPuzzles
#FunctionFiesta
#GraphGoals
#CalcReady
#PreCalcLife
#AlgebraicAdventures
#DerivativeDreams
#IntegrationInsights
#MathematicsMagic
#PreCalcReview
#PrecalcConcepts
#LogarithmLove
#TrigonometryTips
#MathMastermind
#APCalcPrep
#Mathematics
#MathMinds
#Math
#Maths #math #shorts #funny #help #onlineclasses #onlinelearning #online #study