14.1, 14.2 (PC 4.5 & 4.6): Graphing Trig Functions

HW: p.912 (3-5 all)HW tomorrow: p.913 (6, 10, 16, 18), p.919

(12-16 even)Quiz 14.1, 14.2: Tuesday, 5/19

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.)

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 =

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 sinxy 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)( 32cos2)( xxf

Sketch two periods of the graph.

4sin)(

xxfxxf 2cos)(

Sketch one period of the graph.

42cos

3

2 xy 26sin3 xy

14.1, 14.2 (PC 4.5 & 4.6): Graphing Trig Functions

HW: p.913 (20, 24), p.920 (22-32 even, 36, 38)

Quiz 14.1, 14.2: Tuesday, 5/19

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 x-axis of .

)tan( cbxay

xy tan

xy tan

2

cbx

2

cbx

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

2tan2)(

xxf

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

44cot1.0)(

xxf

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