# T.3 - Trig Function Characteristics

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

a)  state the domain and the range of the function;

b)  determine the amplitude, period, phase shift, vertical shift, and asymptotes;

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

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

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - T.3 Understanding

·  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.3b1  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.3d1  Describe the effect of changing A, B, C, or D in the standard form of a trigonometric equation.

·  T.3a1  State the domain and the range of a trigonometric function written in standard form.

·  T.3c1  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