Finding the Mathematical Model of a Sinusoid Y = K + A sin(D(X-H)) Using SNDDEMO data recorded as volts vs time.

Slides:

Advertisements

Similar presentations

Mathematics Mrs. Sharon Hampton. VOCABULARY Lower extreme: the minimum value of the data set Lower quartile: Q1 the median of the lower half of the data.

Advertisements

1 Graphs of sine and cosine curves Sections 10.1 – 10.3.

10.5 Write Trigonometric Functions and Models What is a sinusoid? How do you write a function for a sinusoid? How do you model a situation with a circular.

Graphing Sine and Cosine. Graphing Calculator Mode— Radians Par Simul Window— –X min = -1 –X max = 2  –X scale =  /2 Window— –Y min = -3 –Y max = 3.

Lesson 17 Intro to AC & Sinusoidal Waveforms

4.5 Sinusoidal Graphs Sketching and Writing Equations.

4-4 Graphing Sine and Cosine

Copyright © 2014, 2010, 2007 Pearson Education, Inc Graphs of Other Trigonometric Functions Objectives: Understand the graph of y = sin x. Graph.

Quiz Find a positive and negative co-terminal angle with: co-terminal angle with: 2.Find a positive and negative co-terminal angle with: co-terminal.

Finding the Equation of a Quadratic Using QUADDATA recorded by rolling a ball up and down a ramp. The distance is measured from an arbitrary starting.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 4 Graphs of the Circular Functions Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1.

Today you will use shifts and vertical stretches to graph and find the equations of sinusoidal functions. You will also learn the 5-point method for sketching.

Introduction As we saw in the previous lesson, we can use a process called regression to fit the best equation with the data in an attempt to draw conclusions.

Graphs of the Sine and Cosine Functions Section 6.

January 24 th copyright2009merrydavidson. y = cos x.

Objectives: 1. To identify quadratic functions and graphs 2. To model data with quadratic functions.

This is the graph of y = sin xo

Period and Amplitude Changes

Advanced Algebra II Notes 3.5 Residuals Residuals: y-value of data point – y-value on the line Example: The manager of Big K Pizza must order supplies.

Notes Over 14.5 Writing Trigonometric Functions Write a function for the sinusoid. Positive Sine graph No vertical or horizontal shifts Amplitude: Period:

CHAPTER 4 – LESSON 1 How do you graph sine and cosine by unwrapping the unit circle?

13.1 – Exploring Periodic Data

Section 5.3 Trigonometric Graphs

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 4 Graphs of the Circular Functions Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1.

Homework Questions? Discuss with the people around you. Do not turn in Homework yet… You will do it at the end of class.

Section 4.5 Graphs of Sine and Cosine. Overview In this section we first graph y = sin x and y = cos x. Then we graph transformations of sin x and cos.

Finding a Linear Equation and Regression Finding a Linear Equation Using the LINDEMO data as a Distance in meters from the motion detector vs Time in seconds.

For all work in this unit using TI 84 Graphing Calculator the Diagnostics must be turned on. To do so, select CATALOGUE, use ALPHA key to enter the letter.

EXAMPLE 1 Graph a vertical translation Graph y = 2 sin 4x + 3. SOLUTION STEP 1 Identify the amplitude, period, horizontal shift, and vertical shift. Amplitude:

Chapter 14 Day 8 Graphing Sin and Cos. A periodic function is a function whose output values repeat at regular intervals. Such a function is said to have.

Finding an Exponential Regression Use the data in the program file COOL to find an exponential model.

Section 4.5 Graphs of Sine and Cosine Functions. The Graph of y=sin x.

Periodic Function Review

Section 4.5 Graphs of Sine and Cosine. Sine Curve Key Points:0 Value: π 2π2π π 2π2π 1.

Periodic Functions A periodic function is a function for which there is a repeating pattern of y-values over equal intervals of x. Each complete pattern.

Graphs of Trigonometric Functions Digital Lesson.

1.8 Quadratic Models Speed (in mi/h) Calories burned Ex. 1.

Writing Equations of Trigonometric Graphs Dr. Shildneck Fall.

WARM UP State the sign (positive or negative) of the function in each quadrant. 1. cos x 2. tan x Give the radian measure of the angle ° °

Label each of the following graphs with the appropriate function. Calculator should be set to radians. Window Xscl should be set to pi. The amplitude equals:

Copyright © 2009 Pearson Addison-Wesley The Circular Functions and Their Graphs.

14-1 Graphing the sine, cosine, and tangent functions 14-2 Transformations of the sine, cosine, and tangent functions.

Essential Question: How do we graph trig functions, their transformations, and inverses? Graphs of Sine and Cosine.

Lesson 14: Introduction to AC and Sinusoids

13.1 – Exploring Periodic Data

2.7 Sinusoidal Graphs; Curve Fitting

Writing Equations of Trigonometric Graphs

Sine Equation on TI.

1.6 Trigonometric Functions, p. 46

Periodic Functions.

6.5 – Translation of Sine and Cosine Functions

Writing Equations of Trigonometric Graphs

Chapter 7/8: Sinusoidal Functions of Sine and Cosine

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Graphs of Sine and Cosine

1.6 Trig Functions Greg Kelly, Hanford High School, Richland, Washington.

1.6 Trig Functions Greg Kelly, Hanford High School, Richland, Washington.

M3U7D3 Warm Up Shifted up one Stretched by 3 times

Sine Waves Part II: Data Analysis.

Sine Waves Part II: Data Analysis.

Sinusoidal Functions.

1.6 Trigonometric Functions

Writing Trig Functions

On the unit circle, which radian measure represents the point located at (− 1 2 , − 3 2 )? What about at ( 2 2 , − 2 2 )? Problem of the Day.

Graphs of Sine and Cosine: Sinusoids

Sinusoidal Functions of Sine and Cosine

Section 4.5 Graphs of Sine and Cosine Functions

Section 5.5 Graphs of Sine and Cosine Functions

9.6 Modeling with Trigonometric Functions

Section 4.5 Graphs of Sine and Cosine

Presentation transcript:

Finding the Mathematical Model of a Sinusoid Y = K + A sin(D(X-H)) Using SNDDEMO data recorded as volts vs time.

Finding the Mathematical Model of a Sinusoid Step 1: Find a local maximum and minimum point near the start of the data using the TRACE function.

Finding the Mathematical Model of a Sinusoid Step 2: Find a local maximum and minimum point near the end of the data. Record the values.

Finding the Mathematical Model of a Sinusoid Find the vertical shift (k) value. Step 3: The vertical shift is the midline of the data set. It can be approximated by averaging the local maximum and minimum values. The midline value (k) is volts. Graphing the midline value (y = 2.70) on the current data set.

Finding the Mathematical Model of a Sinusoid Find the amplitude (a) value. Step 4: The amplitude is the maximal change in the data from the midline. To find the amplitude: Subtract the midline from the local maximum value. The amplitude is volts.

Finding the Mathematical Model of a Sinusoid Find the period and frequency. Step 5: Find two local max/min values. Find the difference of the x-coordinates. ( ) =.1425 sec Count the number of cycles from the starting to ending point. 2 cycles Divide the difference by the number of cycles to determine the period seconds/cycle or a period of Find the reciprocal of the period for the frequency cps

Finding the Mathematical Model of a Sinusoid Find the horizontal stretch/shrink (d) value. Step 6: The d value in the model is the number of times the period repeats in 2  radians. The horizontal stretch/shrink (d) value is radians / second.

Finding the Mathematical Model of a Sinusoid Find the horizontal shift (h) value. Step 7: A period of sine begins when the graph crossing the midline with increasing value. The red circle is the beginning of one period of sine. Find the x- value of this point. Average the x-values of the adjacent minimum and maximum values. The horizontal shift is seconds.

Finding the Mathematical Model of a Sinusoid Graph the model y = k + a sin(d(x - h)). Step 8: Enter the values found into the function grapher: k = v a = v d = rad/sec h = sec

Finding the Mathematical Model of a Sinusoid Using the TI-83 SinReg function. Press the STAT key. Use the arrow keys to select CALC and SinReg. Press ENTER. Enter the list for the y-values (L2) followed by a comma. Enter the list for the x-values (L1) followed by a comma. Press VARS followed by Y-VARS and Function... Enter the function to store the regression. (Y2)

Finding the Mathematical Model of a Sinusoid Using the TI-83 SinReg function. The screen should now appear similar to: Press ENTER and the calculator will attempt to determine the regression equation in the form of y = a*sin(bx+c)+d. The resulting model is: The model is stored in the function grapher Y2:

Finding the Mathematical Model of a Sinusoid Using the TI-83 SinReg function. The graph will appear similar to: The two models are: V = v * sin( rad/sec * T sec sec ) v or V = v v * sin( rad/sec (T sec sec )