Math - 2018-19
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
· 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).
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.
the effect of changing A, B, C,
or D in the standard form of a
the domain and the range of a trigonometric function written in standard form.
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