Do Now:

4.5 and 4.6: Graphing Trig Functions

Function table:When you first started graphing linear

functions you may recall having used the following table to graph.

x -2 -1 0 1 2f(x)

Function Table:We will still pick convenient x values. Our

values will be in radians. Lets try the sine function first.

2

2

3 20

Graph y = sin(x):

Graph of y = sin xSine graph is periodic (period for y = sin x is ).2

Five Key Points:

Intercepts, Max,

and Min. Amplitude = half

the distance bet.

the max. and min.

(amplitude for y = sin x is 1.)

Function Table:We will still pick convenient x values. Our

values will be in radians. Lets try the sine function first.

2

2

3 20

Graph y = cos(x):

Graph of y = cos xCosine graph is periodic (period for y = cos x is ).2

Five Key Points:

Intercepts, Max,

and Min. Amplitude = half

the distance bet.

the max. and min.

(amplitude for y = cos x is 1.)

Graphing:Amplitude =

Period = Divide the period by 4 to get four equal subintervals.

Phase Shift : solve equations and .

This will give you the left and right endpoints of a period.

Vertical Shift =

The graph of is a reflection in the x-axis of .

)sin( cbxady

)cos( cbxady a

b

2

d

xy sin xy sin

0 cbx 2 cbx

Find the period and amplitude of the graph.

1.)

2.)

3.)

xy sin3

2cos

2

5 xy

xy cos3

2

Sketch one period of the graph.xxf sin2)( )42cos(3)( xxf

Sketch one period of the graph.

4sin)(

xxfxxf 2cos)(

Sketch one period of the graph.

42cos

3

2 xy 26sin3 xy

Closing: What are the steps for graphing a sin and

cosine function?

Homework:Packet

1-14 even; 39, 40,45, 46, 50, 51

Function Table:Lets try the tangent function.

2

2

3 20x

tan(x)

Graph of y = tan xTangent graph is periodic (period for y = tan x is ).

Vertical asymptotes =

X-intercepts =

n

2

n

Graphing:Asymptotes = solve equations and

.

X-intercept: half way between asymptotes.Period = distance between two consecutive

asymptotes.

The graph of is a reflection in the y-axis of .

)tan( cbxay

xy tan

xy tan

2

cbx

2

cbx

Sketch one period of the graph.xxf 2tan3)(

2tan2)(

xxf

table:Fill in the table for cot(x) and compare it to

tan(x).

2

2

3 20x

tan(x)

Graph of y = cot xCotangent graph is periodic (period for y = cot x is ).

Vertical asymptotes =

X-intercepts = n

2

n

Graphing:Asymptotes = solve equations and

.

X-intercept: half way between asymptotes.Period = distance between two consecutive

asymptotes.

The graph of is a reflection in the y-axis of .

)cot( cbxay

xy cot

xy cot

0 cbx cbx

Sketch one period of the graph.

3cot2)(x

xf

Graphing Cosecant and SecantCosecant: graph sine first.

Where sin x = 0, csc x has a vertical asymptote.Secant: graph cosine first.

Where cos x = 0, sec x has a vertical asymptote.

Sketch one period of the graph.xxf 2sec)(

4csc2)(

xxf

Sketch one period of the graph. xxf 2sec

2

1)(

2csc)(x

xf

Homework:Worksheet

9 – 29 odd