Trigonometric Graphing

Day 1What do the graphs look like?

Sin x

2

3

2

2

3

2

2

1

-1

2

x y

Lets plot some points

1

0

1

0

0 0

Now connect the dots 2Period

Graph does continue

Amplitude

= 1

Cos x

2

3

2

2

3

2

2

1

-1

2

x y

Lets plot some points

0

1

0

1

0 1

Now connect the dots 2Period

Graph does continue

Amplitude

= 1

Tan x

2

3

2

2

3

2

2

1

-1

2

x y

Lets plot some points

Und

0

Und

0

0 0

Now connect the dots Period

Graph does continue

2

Asymptote

Shifts Sin x

y sinx 1

(y n xsi )2

y 2sinx

2

3

2

2

1

-1

y sin2x

y sinxFlips Graph

Shifts up/down

2

Shifts

left/right

2

Inc or Dec Amplitude

Inc or Dec Period

Basic Truths

The period (that is, cycle length) of both y = sin x and y = cos x is 2π.

The amplitude of both functions is 1.

For a standard, we start both of these functions at x = 0 and finish at x = 2π.

So what trends do we observe?Add outside?

Move graph Add inside?

Moves graph Multiply outside?

Changes AmplitudeMultiply inside?

Changes Period 2coeff of x

Do I have to memorize these?

Well, to a degree you should know what to expect. Some teachers want you to look at the graph, determine where it will start and end, determine what the amplitude is, then just graph.

I will teach you a mathematical method that you can memorize.

sin( )y a bx h k

Equation

Change Amplitude

Changes Period

Moves left or Right

Moves up or down

Can substitute any Trig Function

My Method

1. Determine New Start: Set Argument = 02. Determine New End: Set Argument = 2π (or New Start + Period)3. Find 3 midpoints4. Plot these 5 points

Now lets Graph it!

3

2

2

Shift= 2

Shift = +1

Amp

Period

Phase

Vertical

3

4

5

4

1

-1

Period

2

3sin(2 ) 1y x

New Start and Finish

2 0

(2 ) 2

x

and

x

3

2

4

-2

Amp= 3

Now lets Graph it!

9

8

5

4

11

8

1

-1

4Period

2

y tan(4x 4 ) 1

sinRemember Tan= therefore we will have asymptotes when???

cos

3

2