function given: y=sin(2x-π/2)Problem 1: Use the 5 step process given in Section 5.5 to find the 5 key points for graphing your function. Label the steps, give necessary formulas, and show work for finding and reporting the amplitude, period, and phase shift. Examples 4 and 6 in section 5.5 can be very helpful with the level of detail required.Make a hand sketch for 1 period of your function and add it to the Word Document.Problem 2: Consider y= tan( x- π4)Use the 4 step process given in Section 5.6 to find and give the asymptotes, x-intercepts, quarter points and three-quarter points for two consecutive asymptotes for graphing. Label the steps, give necessary formulas, and show work. Example 2 in section 5.6 can be very helpful with the level of detail required.Make a hand sketch for 2 periods of your function and add it to the Word Document.Use one of the graphing tools (Desmos or Graphmatica) graph the function and compare to your hand sketch.Problem 3:Use reference angles and the 2 step process in Section 5.3 to find the exact value of each expression. Include a hand drawn sketch to show (and label) the reference angle like in Examples 7 and 8. Drawing sketches insure you have the correct signs for answers. Do not use a calculator to just write the answer.sec510 °cot11π6Problem 4:If tanθ=74 and sinθ<0, find the following. Include a hand drawn sketch like in Ch 5.3 Example 4 to help show your work. Do not use a calculator to just write the answer.cosθcscθ E MyLab Math Pearson eTextPearson eTextb bartleby - Bingb function given: y=sin(2x-T/2) Pr. xC Given Function: Y=sin(2x- 1/2)C Your Problem 1: Use The 5 Step xA Desmos | Graphing CalculatorÔ https://etext-ise.pearson.com/courses/5785797/products/110273/pages/630?locale=&platformld=1030&isTpi=Y&iesCode%=LZDU9BKQQW...604ContentsContentsВMATH 143 Precalculus Essentials - Feb2021 - OnlineAmplitudes and PeriodsThe graph of y = A sin Bx, B > 0, hasHistoryy = A sin BxAlgebra and Trigonometryamplitude = |A|BY ROBERT BLITZERBperiod =ВNotebookChapter 3 Polynomial and Rational FunctionsAmplitude: JA|Chapter 4 Exponential and LogarithmicFunctionsPeriod:Chapter 5 Trigonometric FunctionsEXAMPLE 3Graphing a Function of the Form y = A sin BxChapter 6 Analytic TrigonometryDetermine the amplitude and period of y = 3 sin 2x. Then gra0sx< 2m.the function forChapter 7 Additional Topics in TrigonometrySOLUTIONChapter 8 Systems of Equations and InequalitiesStep 1 Identify the amplitude and the period. The equation y = 3 sin 2x is of theform y = A sin Bx with A = 3 and B = 2.Chapter 9 Matrices and Determinantsamplitude:|A| = |3| = 327period:= TTChapter 10 Conic Sections and AnalyticВGeometryThe amplitude, 3, tells us that the maximum value of y is 3 and the minimum valueof y is -3. The period, 7, tells us that the graph completes one cycle from 0 to .Chapter 11 Sequences, Induction, andStep 2 Find the values of x for the five key points. Begin by dividing the periodof y = 3 sin 2x, 7, by 4.ProbabilityperiodTTAppendix: Where Did That Come From? Selected Proofs44Start with the value of x where the cycle begins: x1 = 0. Adding quarter-periods,the five x-values for the key points areAnswers to Selected Exercises4TX = 0, x, = 0 +4TTTTX3 =Subject Index42'37X4 =2.X5 =4%3DT.Photo Credits44.Definitions, Rules, and Formulas7:44 PMP Type here to searchA O a 4)3/10/2021...近> E MyLab Math Pearson eTextPearson eTextb bartleby - Bingb function given: y=sin(2x-T/2) Pr. xC Given Function: Y=sin(2x- T/2) |C Your Problem 1: Use The 5 StepA Desmos | Graphing CalculatorÔ https://etext-ise.pearson.com/courses/5785797/products/110273/pages/631?locale=&platformld=1030&isTpi=Y&iesCode%=LZDU9BKQQW...605ContentsContentsMATH 143 Precalculus Essentials - Feb2021 - OnlineSection 5.5 Graphs of Sine and Cosine Functions 605HistoryStep 3 Find the values of y for the five key points. We evaluate the function ateach value of x from step 2.Algebra and TrigonometryBY ROBERT BLITZERNotebookChapter 3 Polynomial and Rational FunctionsValue of xValue of y: y = 3 sin 2rCoordinates of key pointy = 3 sin (2 · 0)= 3 sin 0 = 3 0 = 0Chapter 4 Exponential and Logarithmic(0, 0)Functionsy = 3 sin 2..maximum()Chapter 5 Trigonometric Functionspoint4= 3 sin = 3.1= 3Chapter 6 Analytic Trigonometryy = 3 sin 2 .2Chapter 7 Additional Topics in Trigonometry= 3 sin 7 = 3.0 = 037y = 3 sin (2.(-)Chapter 8 Systems of Equations and Inequalities37minimum4y = 3 sin 2r= 3 sin= 3(-1) = -3pointChapter 9 Matrices and Determinantsy = 3 sin (2· T)= 3 sin 27 = 3.0 = 0(7, 0)Chapter 10 Conic Sections and AnalyticGeometryIn the interval [0, 7), there are x-intercepts at 0,", and . The maximum andminimum points are indicated by the voice balloons.Chapter 11 Sequences, Induction, andStep 4 Connect the five key points with a smooth curve and graph one completecycle of the given function. The five key points for y = 3 sin 2r are shown inFigure 5.69. By connecting the points with a smooth curve, the blue portion showsone complete cycle of y = 3 sin 2x from 0 to 7. The graph of y = 3 sin 2x is thegraph of y = sin x vertically stretched by a factor of 3 and horizontally shrunk byProbabilityFIGURE 5.69 The graphof y = 3 sin 2x, 0 s xs TAppendix: Where Did That Come From? Selected Proofs1a factor ofy = 3 sin 2rAnswers to Selected ExercisesStep 5 Extend the graph in step 4 to the left or right as desired. The blue portionof the graph in Figure 5.69 is from 0 to 7. In order to graph for 0 近

Given: y=sin2x-π2To Find: AmplitudePeriodPhase Shift Concept:…

Answered: function given: y=sin(2x-π/2) Problem…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

function given: y=sin(2x-π/2)

Problem 1: Use the 5 step process given in Section 5.5 to find the 5 key points for graphing your function. Label the steps, give necessary formulas, and show work for finding and reporting the amplitude, period, and phase shift. Examples 4 and 6 in section 5.5 can be very helpful with the level of detail required.

Make a hand sketch for 1 period of your function and add it to the Word Document.

Problem 2: Consider y= tan( x- π4)

Use the 4 step process given in Section 5.6 to find and give the asymptotes, x-intercepts, quarter points and three-quarter points for two consecutive asymptotes for graphing. Label the steps, give necessary formulas, and show work. Example 2 in section 5.6 can be very helpful with the level of detail required.

Make a hand sketch for 2 periods of your function and add it to the Word Document.

Use one of the graphing tools (Desmos or Graphmatica) graph the function and compare to your hand sketch.

Problem 3:

Use reference angles and the 2 step process in Section 5.3 to find the exact value of each expression. Include a hand drawn sketch to show (and label) the reference angle like in Examples 7 and 8. Drawing sketches insure you have the correct signs for answers. Do not use a calculator to just write the answer.

sec510 °
cot11π6

Problem 4:

If tanθ=74 and sinθ<0, find the following. Include a hand drawn sketch like in Ch 5.3 Example 4 to help show your work. Do not use a calculator to just write the answer.

cosθ
cscθ

E MyLab Math Pearson eText
Pearson eText
b bartleby - Bing
b function given: y=sin(2x-T/2) Pr. x
C Given Function: Y=sin(2x- 1/2)
C Your Problem 1: Use The 5 Step x
A Desmos | Graphing Calculator
Ô https://etext-ise.pearson.com/courses/5785797/products/110273/pages/630?locale=&platformld=1030&isTpi=Y&iesCode%=LZDU9BKQQW
...
604
Contents
Contents
В
MATH 143 Precalculus Essentials - Feb
2021 - Online
Amplitudes and Periods
The graph of y = A sin Bx, B > 0, has
History
y = A sin Bx
Algebra and Trigonometry
amplitude = |A|
BY ROBERT BLITZER
B
period =
В
Notebook
Chapter 3 Polynomial and Rational Functions
Amplitude: JA|
Chapter 4 Exponential and Logarithmic
Functions
Period:
Chapter 5 Trigonometric Functions
EXAMPLE 3
Graphing a Function of the Form y = A sin Bx
Chapter 6 Analytic Trigonometry
Determine the amplitude and period of y = 3 sin 2x. Then gra
0sx< 2m.
the function for
Chapter 7 Additional Topics in Trigonometry
SOLUTION
Chapter 8 Systems of Equations and Inequalities
Step 1 Identify the amplitude and the period. The equation y = 3 sin 2x is of the
form y = A sin Bx with A = 3 and B = 2.
Chapter 9 Matrices and Determinants
amplitude:
|A| = |3| = 3
27
period:
= TT
Chapter 10 Conic Sections and Analytic
В
Geometry
The amplitude, 3, tells us that the maximum value of y is 3 and the minimum value
of y is -3. The period, 7, tells us that the graph completes one cycle from 0 to .
Chapter 11 Sequences, Induction, and
Step 2 Find the values of x for the five key points. Begin by dividing the period
of y = 3 sin 2x, 7, by 4.
Probability
period
TT
Appendix: Where Did That Come From? Selected Proofs
4
4
Start with the value of x where the cycle begins: x1 = 0. Adding quarter-periods,
the five x-values for the key points are
Answers to Selected Exercises
4
T
X = 0, x, = 0 +
4
TT
TT
X3 =
Subject Index
4
2'
37
X4 =
2.
X5 =
4
%3D
T.
Photo Credits
4
4.
Definitions, Rules, and Formulas
7:44 PM
P Type here to search
A O a 4)
3/10/2021
...
近
>

E MyLab Math Pearson eText
Pearson eText
b bartleby - Bing
b function given: y=sin(2x-T/2) Pr. x
C Given Function: Y=sin(2x- T/2) |
C Your Problem 1: Use The 5 Step
A Desmos | Graphing Calculator
Ô https://etext-ise.pearson.com/courses/5785797/products/110273/pages/631?locale=&platformld=1030&isTpi=Y&iesCode%=LZDU9BKQQW
...
605
Contents
Contents
MATH 143 Precalculus Essentials - Feb
2021 - Online
Section 5.5 Graphs of Sine and Cosine Functions 605
History
Step 3 Find the values of y for the five key points. We evaluate the function at
each value of x from step 2.
Algebra and Trigonometry
BY ROBERT BLITZER
Notebook
Chapter 3 Polynomial and Rational Functions
Value of x
Value of y: y = 3 sin 2r
Coordinates of key point
y = 3 sin (2 · 0)
= 3 sin 0 = 3 0 = 0
Chapter 4 Exponential and Logarithmic
(0, 0)
Functions
y = 3 sin 2..
maximum
()
Chapter 5 Trigonometric Functions
point
4
= 3 sin = 3.1= 3
Chapter 6 Analytic Trigonometry
y = 3 sin 2 .
2
Chapter 7 Additional Topics in Trigonometry
= 3 sin 7 = 3.0 = 0
37
y = 3 sin (2.
(-)
Chapter 8 Systems of Equations and Inequalities
37
minimum
4
y = 3 sin 2r
= 3 sin
= 3(-1) = -3
point
Chapter 9 Matrices and Determinants
y = 3 sin (2· T)
= 3 sin 27 = 3.0 = 0
(7, 0)
Chapter 10 Conic Sections and Analytic
Geometry
In the interval [0, 7), there are x-intercepts at 0,", and . The maximum and
minimum points are indicated by the voice balloons.
Chapter 11 Sequences, Induction, and
Step 4 Connect the five key points with a smooth curve and graph one complete
cycle of the given function. The five key points for y = 3 sin 2r are shown in
Figure 5.69. By connecting the points with a smooth curve, the blue portion shows
one complete cycle of y = 3 sin 2x from 0 to 7. The graph of y = 3 sin 2x is the
graph of y = sin x vertically stretched by a factor of 3 and horizontally shrunk by
Probability
FIGURE 5.69 The graph
of y = 3 sin 2x, 0 s xs T
Appendix: Where Did That Come From? Selected Proofs
1
a factor of
y = 3 sin 2r
Answers to Selected Exercises
Step 5 Extend the graph in step 4 to the left or right as desired. The blue portion
of the graph in Figure 5.69 is from 0 to 7. In order to graph for 0 <x s 2n, we
continue this portion and extend the graph another full period to the right. This
extension is shown in gray in Figure 5.70.
Subject Index
Photo Credits
O Check Point 3 Determine the amplitude and period of y = 2 sinx. Then
øraph the function for 0 < r< 8T.
Definitions, Rules, and Formulas
FIGURE 5.7O
7:45 PM
P Type here to search
A O G 4)
3/10/2021
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