#### Math - 2019-20

# T.3 - Trig Function Characteristics

T.3The student, given one of the six trigonometric functions in standard form, will

a) statethe domain and the range of the function;

b) determinethe amplitude, period, phase shift, vertical shift, and asymptotes;

c) sketchthe graph of the function by using transformations for at least a two-period interval;

d)investigatethe effect of changing the parameters in a trigonometric function on the graph of the function.

*Adopted: 2016*

### BIG IDEAS

### UNDERSTANDING THE STANDARD

· The domain and range of a trigonometric function determine the scales of the axes for the graph of the trigonometric function.

· The amplitude, period, phase shift, and vertical shift are important characteristics of the graph of a trigonometric function, and each has a specific purpose in applications using trigonometric equations.

· The graph of a trigonometric function can be used to display information about the periodic behavior of a real-world situation, such as wave motion or the motion of a Ferris wheel.

· Standard form of the trigonometric functions may be written in multiple ways (e.g.,*y*=

*A*sin (

*Bx*+

*C*) +

*D*or

*y*=

*A*sin [

*B*(

*x*+

*C*)] +

*D*).

### ESSENTIALS

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

·
T.3b_{1}** Determine**
the amplitude, period, phase shift, vertical shift, and asymptotes of a
trigonometric function from the equation of the function and from the graph of
the function.

·
T.3d_{1}** Describe**
the effect of changing *A*, *B*, *C*,
or *D* in the standard form of a
trigonometric equation.

·
T.3a_{1}** State**
the domain and the range of a trigonometric function written in standard form.

·
T.3c_{1}** Sketch**
the graph of a function written in standard form by using transformations for
at least a two-period interval, including both positive and negative values for
the domain.

### KEY VOCABULARY

*Updated: Jun 06, 2018*