Geometry/Trig

Name: _________________________________

Date: _________________________

9-7: Identifying Vertical Shifts

Learning Goal:

#1: How do we identify characteristics for a trigonometric equation? #2: How do we identify vertical

shifts of a trigonometric function?

Warm Up: Name the amplitude, period, and frequency of the following graphs and equations.

1.

2.

3. 3sin(2 ) 1y

New Formula alert!!!

To find a vertical shift given a graph we must find the midline:

Midline =

Amplitude:_____________

Period:______________

Frequency:_______________

Amplitude:_____________

Period:______________

Frequency:_______________

Amplitude:_____________

Period:______________

Frequency:_______________

Geometry/Trig

Let’s Try One:

Find the vertical shift in shown in the accompanying diagram.

You Try Some:

Find the vertical shifts shown in the accompanying diagrams.

Vertical Shift:__________________________

Vertical Shift:__________________________

Vertical Shift:__________________________

Vertical Shift:__________________________

Geometry/Trig

Putting It All Together!

Find the amplitude, period, frequency, and vertical shift of the following graphs. After finding these

characteristics, write the equation to the graph shown.

1.

2.

Amplitude:____________________

Period:_______________________

Frequency:_____________________

Vertical Shift:_____________________

Equation of sine:

___________________________________

Amplitude:____________________

Period:_______________________

Frequency:_____________________

Vertical Shift:_____________________

Equation of sine:

___________________________________

Geometry/Trig 3.

4.

Amplitude:____________________

Period:_______________________

Frequency:_____________________

Vertical Shift:_____________________

Equation of cosine:

___________________________________

Amplitude:____________________

Period:_______________________

Frequency:_____________________

Vertical Shift:_____________________

Equation of cosine:

___________________________________

Geometry/Trig

Practice:

1. Find the amplitude, period, frequency, and the vertical shift of the following equations.

2. ( ) Amplitude

Frequency

Period Vertical Shift

3.

( )

Amplitude Frequency Period Vertical Shift

4. ( )

Amplitude Frequency Period Vertical Shift

5. List the critical values of ( ):

6. Graph ( ) from 0 to . Use the critical values above to assist you in graphing the function.

Hint: Be sure to label your x and

y axis before you begin to plot

your critical values!

Geometry/Trig

Name: _________________________________

Date: _________________________

Lesson 9-7: Homework

Directions: For each of the equations, find the amplitude, frequency, period, and vertical shift of the original graph.

1. (

)

Amplitude

Frequency

Period Vertical Shift

2. ( )

( )

Amplitude Frequency Period Vertical Shift

3. ( ) Amplitude Frequency Period Vertical Shift

4. Below is a graph of a trig function:

a. List the critical values that are plotted in

the graph to the left.

b. Based on your answer from part a, is

this a sine curve or a cosine curve?

Give an explanation for your answer.

Geometry/Trig

5. List the critical values of ( ):

6. Graph ( ) from 0 to . Use the critical values above to assist you in graphing the function.

7. Convert the following radian measures to degrees:

8. Convert the following degree measures to radians:

75˚ 300˚ 225˚