Trigonometry B Ms. DiGilio - 2013 Calendar & Notes Packet

Unit 5 – CHAPTER 4: Graphing

Monday Tuesday Wednesday Thursday Friday April 8.

9.

10.

11. Intro to

Sine/Cosine Graphs

(Amplitude)

HW: Day 1 WS

12. Sine/Cosine

Graphs (Period Changes + Vertical Shifts)

HW: Day 2 WS

(#1 - #14) 15.

Sine/Cosine Graphs

(Horizontal Shifts)

HW: Day 3 WS

16.

Intro to Secant/Cosecant

Graphs

HW: Day 4 WS

17. Secant/Cosecant

Graphs Part 2

HW: Day 5 WS

18.

Review sin/cos/sec/csc

Graphs

HW: Review Packet

19.

QUIZ: Graphing sin/cos/sec/csc

HW: none ☺

22. Intro to Cotangent

Graphs

HW: Day 6 WS

23. NO CLASSES

Juniors: ACT

*GOOD LUCK! *

24. NO CLASSES

Juniors: PSAE

*GOOD LUCK! *

25.

Intro to Tangent Graphs

HW: Day 7 WS

26.

Chart of all Transformations &

Review

HW: Review Packet

29. TEST

CHAPTER 4

Graphing all 6 Trig Functions

HW: none ☺

30.

Chapter 2 � (Bearing)

May 1. 2. 3.

This calendar is subject to change – please refer to class discussions for exact homework assignments.

Trigonometry B: Unit 5: Chapter 4 – Graphing Trig Equations Date: Notes – Day 1: Basic Sine & Cosine Graph + Amplitude Changes * When graphing trig functions...

The x-axis (______________) will represent the _______________________

The y-axis (______________) will represent the _______________________

* PART I: Let's fill in the following table for the function: f(x) = sin(x)

x sin(x) x sin(x)

0

/ 6π 7 / 6π

/ 4π 5 / 4π

/ 3π 4 / 3π

/ 2π 3 / 2π

2 / 3π 5 / 3π

3 / 4π 7 / 4π

5 / 6π 11 / 6π

π 2π

* Now plot the above points and connect. What kind of shape is formed? Period: Amplitude: Domain: Range:

** Refer to your Unit Circle**

* Vocabulary to be familiar with when graphing: DOMAIN ���� RANGE ���� PERIOD ���� AMPLITUDE ���� CRITICAL VALUES ���� * PART II: Let's fill in the following table for the function: f(x) = cos(x)

x cos(x) x cos(x)

0

/ 6π 7 / 6π

/ 4π 5 / 4π

/ 3π 4 / 3π

/ 2π 3 / 2π

2 / 3π 5 / 3π

3 / 4π 7 / 4π

5 / 6π 11 / 6π

π 2π

Period: Amplitude: Domain: Range:

** Refer to your Unit Circle**

3

-3

**AMPLITUDE CHANGES** * Fill in the following charts and graph each function in a different color. Sine Parent Graph What happens to the following functions??

x sin(x)

0

/ 2π

π

3 / 2π

2π

* So in summary, to change the amplitude, ________________________________________

( ) sin( )f x a x= * How did the graph change when a NEGATIVE sign was in front of the trig function?

x 3sin(x)

0

/ 2π

π

3 / 2π

2π

x -2sin(x)

0

/ 2π

π

3 / 2π

2π

x 0.5sin(x)

0

/ 2π

π

3 / 2π

2π

2π

* Day 1 Examples � Sine & Cosine with Amplitude Changes Ex. 1) ( ) 2sinf x x= Period: Amplitude: Domain: Range: Ex. 2) ( ) 3sinf x x= −

Period: Amplitude: Domain: Range: Ex. 3) ( ) 4cosf x x=

Period: Amplitude: Domain: Range:

Ex. 4) 1

( ) sin2

f x x=

Period: Amplitude: Domain: Range:

Ex. 5) 1

( ) sin3

f x x= −

Period: Amplitude: Domain: Range: Ex. 6) ( ) 15sinf x x= Period: Amplitude: Domain: Range:

1

-1

Trigonometry B: Unit 5: Chapter 4 – Graphing Trig Equations Date: Notes – Day 2: Sine & Cosine Graph Period & Vertical Changes

**PERIOD CHANGES**

* Fill in the following charts and graph each function in a different color. Sine Parent Graph What happens to the following functions??(Note the input changes)

x sin(x)

0

/ 2π

π

3 / 2π

2π

* So in summary, to change the period, ________________________________________

( ) sin( )f x a bx= * And to calculate the period, compute: Period = So for a sine or cosine graph �

x sin(2x)

0

/ 4π

/ 2π

3 / 4π

π

x sin(4x)

0

/ 8π

/ 4π

3 / 8π

/ 2π

x sin(0.5x)

0

π

2π

3π

4π

4π

* Day 2 Examples � Sine & Cosine with Period Changes Ex. 1) ( ) sin 5f x x= Period: Amplitude: Domain: Range:

Ex. 2) ( ) cos 2f x xπ= Period: Amplitude: Domain: Range:

Ex. 3) 1

( ) sin2

f x x=

Period: Amplitude: Domain: Range:

Ex. 4) ( ) 3sin 2f x x= Period: Amplitude: Domain: Range:

Ex. 5) 1 1

( ) cos2 4

f x x=

Period: Amplitude: Domain: Range: Ex. 6) ( ) 3sin 4f x x= − Period: Amplitude: Domain: Range: Ex. 7) ( ) 2cos10f x x= − Period: Amplitude: Domain: Range:

5

-5

**VERTICAL SHIFTS**

* Fill in the following charts and graph each function in a different color. Sine Parent Graph What happens to the following functions??

x sin(x)

0

/ 2π

π

3 / 2π

2π

* So in order to shift a graph vertically, _____________________________________________

( ) sin( )f x a bx d= ±

* This will change your ______________________!!!!!!

x sin(x)+1

0

/ 2π

π

3 / 2π

2π

x sin(x)+4

0

/ 2π

π

3 / 2π

2π

x sin(x)-2

0

/ 2π

π

3 / 2π

2π

2π

* Day 2 Examples � Sine & Cosine with Vertical Shifts Ex. 1) ( ) sin 3f x x= + Period: Amplitude: Domain: Range:

Ex. 2) ( ) cos 2f x x= − Period: Amplitude: Domain: Range: Ex. 3) ( ) 3sin 1f x x= + Period: Amplitude: Domain: Range:

Ex. 4) ( ) 4 cos 2f x x= + Period: Amplitude: Domain: Range: Ex. 5) ( ) 4sin 3f x xπ= − Period: Amplitude: Domain: Range:

Ex. 6) 1 1

( ) 2 sin2 2

f x x= −

Period: Amplitude: Domain: Range:

Ex. 7) ( ) 5cos 312

f x xπ= −

Period: Amplitude: Domain: Range:

1

-1

2

π−

Trigonometry B: Unit 5: Chapter 4 – Graphing Trig Equations Date: Notes – Day 3: Sine & Cosine Graph Horizontal (Phase) Shifts

**HORIZONTAL (PHASE) SHIFTS**

* Fill in the following charts and graph each function in a different color. Sine Parent Graph What happens to the following functions??(Note the input changes)

x sin(x)

0

/ 2π

π

3 / 2π

2π

* So in summary, in order to phase shift a trig graph (move horizontally), you can

_______________________________________ � ( ) sin[ ( )]f x a b x c d= ± ±

BUT….. _______________________ so always ______________________________

Ex. ( ) 3cos(4 16)f x x= + Ex. ( ) 5sin2 4

f x xπ π = +

x sin(x- / 2π )

/ 2π

π

3 / 2π

2π

5 / 2π

x sin(x+ / 2π )

/ 2π−

0

/ 2π

π

3 / 2π

x sin(x-π )

π

3 / 2π

2π

5 / 2π

3π

3π

* Day 3 Examples � Sine & Cosine with Horizontal (Phase) Changes Ex. 1) ( ) sin( )f x x π= − Period: Amplitude: Domain: Range:

Ex. 2) ( ) cos2

f x xπ = +

Period: Amplitude: Domain: Range:

Ex. 3) ( ) 4cos4

f x xπ = +

Period: Amplitude: Domain: Range:

Ex. 4) ( ) sin( ) 3f x x π= − + − Period: Amplitude: Domain: Range:

Ex. 5) ( ) 4cos4

f x xπ = +

Period: Amplitude: Domain: Range: Ex. 6) ( ) 3sin(2 ) 3f x x π= − + − Period: Amplitude: Domain: Range:

Ex. 7) 1 1

( ) sin (3 ) 22 3

f x x π= − +

Period: Amplitude: Domain: Range:

Trigonometry B: Unit 5: Chapter 4 – Graphing Trig Equations Date: Notes – Day 4: Secant & Cosecant Graphs Two new trig graphs… Something to think about � sin x = cos x = So when we graph these, how is our domain affected? Our graph? * In order to graph f(x) = csc(x) fill in the following table for sin(x) first.

x sin(x) csc(x) x sin(x) csc(x)

0

/ 6π 7 / 6π

/ 4π 5 / 4π

/ 3π 4 / 3π

/ 2π 3 / 2π

2 / 3π 5 / 3π

3 / 4π 7 / 4π

5 / 6π 11 / 6π

π 2π

* Now plot the above points for the graph ( ) cscf x x= . Period: Amplitude: Domain: Range: * Domains: For ANY graph �

For cscx and secx �

* Day 4 Examples � Secant & Cosecant Graphs Ex. 1) ( ) secf x x= Period: Amplitude: Domain: Range:

Ex. 2) ( ) cscf x x= Period: Amplitude: Domain: Range: Ex. 3) ( ) cscf x x= − Period: Amplitude: Domain: Range:

Ex. 4) 1

( ) sec4

f x x=

Period: Amplitude: Domain: Range: Ex. 5) ( ) cscf x xπ= Period: Amplitude: Domain: Range: Ex. 6) ( ) 3csc 4f x x= Period: Amplitude: Domain: Range: Ex. 7) ( ) 2sec 4 2f x x= − + Period: Amplitude: Domain: Range:

Trigonometry B: Unit 5: Chapter 4 – Graphing Trig Equations Date: Notes – Day 5: Secant & Cosecant Graphs Part 2

Ex. 1) ( ) 2sec2

f x xπ= −

Period: Amplitude: Domain: Range:

Ex. 2) ( ) csc( )f x xπ= + Period: Amplitude: Domain: Range: Ex. 3) ( ) sec( )f x xπ= − + Period: Amplitude: Domain: Range:

Ex. 4) 1

( ) csc4 4

f x xπ = +

Period: Amplitude: Domain: Range: Ex. 5) ( ) csc(4 )f x x π= − − Period: Amplitude: Domain: Range:

Ex. 6) 1

( ) sec3 2 2

f x xπ π = +

Period: Amplitude: Domain: Range:

Ex. 7) ( ) 2csc4

f x xπ = − +

Period: Amplitude: Domain: Range:

Trigonometry B: Unit 5: Chapter 4 – Graphing Trig Equations Date: Notes – Day 6: Cotangent Graphs * Let's fill in the following table for the function: f(x) = cot(x)

x cot(x) x cot(x)

0

/ 6π 7 / 6π

/ 4π 5 / 4π

/ 3π 4 / 3π

/ 2π 3 / 2π

2 / 3π 5 / 3π

3 / 4π 7 / 4π

5 / 6π 11 / 6π

π 2π

* Now plot the above points and connect. What kind of shape is formed? Period: Amplitude: Domain: Range:

** Refer to your Unit Circle**

* Day 6 Examples � Cotangent Graphs Ex. 1) ( ) cotf x x= Period: Amplitude: Domain: Range:

Ex. 2) ( ) cot4

xf x =

Period: Amplitude: Domain: Range: Ex. 3) ( ) 8cotf x x= Period: Amplitude: Domain: Range:

Ex. 4) ( ) cot 4f x x= − Period: Amplitude: Domain: Range:

Ex. 5) 1

( ) cot3 4

f x xπ = −

Period: Amplitude: Domain: Range: Ex. 6) ( ) cot 3f x x= + Period: Amplitude: Domain: Range: Ex. 7) ( ) cot 4f x x= − Period: Amplitude: Domain: Range:

Trigonometry B: Unit 5: Chapter 4 – Graphing Trig Equations Date: Notes – Day 7: Tangent Graphs Ex. 1) ( ) tanf x x= Period: Amplitude: Domain: Range:

Ex. 2) ( ) tan2

xf x =

Period: Amplitude: Domain: Range:

Ex. 3) 1

( ) tan3

f x x=

Period: Amplitude: Domain: Range:

Ex. 4) ( ) 3 tanf x xπ= − Period: Amplitude: Domain: Range: Ex. 5) ( ) tan 2f x x= − Period: Amplitude: Domain: Range:

Ex. 6) ( ) tan4

f x xπ = −

Period: Amplitude: Domain: Range:

Ex. 7) 1

( ) tan10 4 4

f x xπ π = +

Period: Amplitude: Domain: Range: