More Trig – Graphing Trig Functions Learning Objective: To graph the sin, cos and tan functions and their

transformations

Warm-up (IN)Evaluate. Give exact values.

3cos 1.

6in 2.

s

3

5cos 3.

4

an 4.

t

4ec 5.

s

6cot 6.

1

21

2 1

21

23

Notes

Learning Objective: To graph the sin, cos and tan functions and their transformations

xy sin

xy cos

Cool graphs!

Learning Objective: To graph the sin, cos and tan functions and their transformations

Trig functions are periodic

- they repeat

Cycle - A portion of the graph of the function from one point on the graph to the point at which the graph starts to repeat itself

Period - The number of degrees taken to complete one cycle

The period of the sin and cos graphs are360˚

Amplitude -The distance from its axis to the highest or lowest point

The amplitude of the sin and cos graphs is 1

Learning Objective: To graph the sin, cos and tan functions and their transformations

sinba hy k or cosa hy b k

a = amplitudeb = horizontal stretch/compression

h = horizontal shift

(phase shift)

(changes period by a

factor of )

k = vertical shift

b

1

Learning Objective: To graph the sin, cos and tan functions and their transformations

Ex 1 - Describe the transformations, then graph at least one period with its parent function.

cos2

1 a. y

The amplitude is 1/2

Learning Objective: To graph the sin, cos and tan functions and their transformations

2sin b. y

The period is

2

1 360

180

Learning Objective: To graph the sin, cos and tan functions and their transformations

45cos c. y

Shifts right 45˚

Learning Objective: To graph the sin, cos and tan functions and their transformations

2sin d. y

Shifts down 2

HW – p. 864

#11-39 ODD

Out – Compare and contrast the graph of with the graph of .

Summary – I have a question about…or… Wow! I…

xy sinxy cos