Chapter 5B – Graphs of Trigonometric Functions

20 Days

5.5 Trigonometric Graphs

Three days

Theorem on Amplitude, Periods, and Phase Shifts

20

:inequality thesolvingby found becan cycle oneexactly containing intervalan (2)

.b

c- isshift phase theand ,

2 is period the, is amplitude the(1)

: thenb, and a numbers real nonzerofor )cos(or )sin( If

cbx

ba

cbxaycbxay

xy sin2 :Graph

xy sin :Graph 21

xy 2sin :Graph

1cos :Graph 21 xy

xy cos2 :Graph

Graphing Sine and Cosine WS

Homework

Begin 5.5.2

Reminder: Theorem on Amplitude, Periods, and Phase Shifts

20

:inequality thesolvingby found becan cycle oneexactly containing intervalan (2)

.b

c- isshift phase theand ,

2 is period the, is amplitude the(1)

: thenb, and a numbers real nonzerofor )cos(or )sin( If

cbx

ba

cbxaycbxay

)cos( :Graph xy

Period:

Amplitude:

Phase shift: Domain:

Range:

22sin2 :Graph

xy

Period:

Amplitude:

Phase shift: Domain:

Range:

14

sin3 :Graph

xy

Period:

Amplitude:

Phase shift: Domain:

Range:

p416 #5,6,9,11,13,14,20 - 22

Homework

Graphing Practice #2 and PreCalculus Dennison p63

Quiz Tomorrow!

Homework

HW for after the quiz: p444 #36,38,40,46,48 hit ‘0’, need y-

intercept

Homework

5.6 Additional Trigonometric Graphs

Four Days

At what angles is the tangent function undefined?

What about the cotangent?

What do you think will be in our graph at those points?

Graphing Tangent and Cotangent

Theorem on Amplitude, Periods, and Phase Shifts

2

2

:inequality thesolvingby found becan cycle oneexactly containing intervalan (2)

.b

c- isshift phase theand , is period the(1)

: thenb, and a numbers real nonzerofor )tan( If

cbx

b

cbxay

cbx

b

cbxay

0

:inequality thesolvingby found becan cycle oneexactly containing intervalan (2)

.b

c- isshift phase theand , is period the(1)

: thenb, and a numbers real nonzerofor )cot( If

xy tan3 :Graph

4tan :Graph xy

2cot :Graph xy

)32tan( :Graph xy

p427 #1,4,9,11,13,16,17,19,21,26

Homework

5.6.2 Graphing Secant and Cosecant

Four Days

2sec :Graph xy

)2sec(2 :Graph xy

2csc :Graph 43 xy

p427 #5,7,31,33,36,40,49,51,52

Homework

6.6.1 Inverse Trig Functions

Four Days

Definition of the Inverse Sine Function

22 and 11for

sin ifonly and if sin

by definded is arcsin,or sin denoted function, sine inverse The

1

1

yx

yxxy

Properties of the sin-1

22

if sinarcsinsinsin .2

11 if arcsinsinsinsin .1

1

1

yyyy

xxxx

Examples

321

31

321

sinsin

sinsin

sinsin

Definition of the Inverse Cosine Function

yx

yxxy

0 and 11for

cos ifonly and if cos

by definded is arccos,or cos denoted function, cosine inverse The

1

1

Properties of the cos-1

yyyy

xxxx

0 if cosarccoscoscos .2

11 if arccoscoscoscos .1

1

1

Examples

31

21

1

sincos

coscos

3.coscos

Find the exact value of

More examples

31arccossin

Definition of the Inverse Tangent Function or Arctangent Function

.22

andnumber x realany for

tan ifonly and if tan

by definded is arctan,or tandenoted function, tangent inverse The

1

1

y

yxxy

Properties of the sin-1

22

if tanarctantan tan.2

allfor arctantantan tan.1

1

1

yyyy

xxxx

Examples

3

111

1

tanarctan

tantan

25tantan

p511 #1 - 15 odd

Homework

p511 #6,10 - 16 even, 24, 25

Homework

6.5 worksheet Inverse functions #1 - 15 odd, 19 - 21

Homework

15.8 & 6.4 Enrichment worksheets on trig inverses

Homework

Homework

Homework

http://etc.usf.edu/clipart/galleries/672-trigonometry-graphs