You analyzed graphs of trigonometric functions.

[Pages:46]You analyzed graphs of trigonometric functions. (Lesson 4-4)

LEQ: How do we graph tangent and reciprocal trigonometric functions & graph damped trigonometric functions?

? damped trigonometric function ? damping factor ? damped oscillation ? damped wave ? damped harmonic motion

Graph Horizontal Dilations of the Tangent Function

Locate the vertical asymptotes, and sketch the graph of y = tan .

The graph of y = tan is the graph of y = tan x

expanded horizontally. The period is or 3. Find two consecutive vertical asymptotes by solving bx + c = ? and bx + c = .

Graph Horizontal Dilations of the Tangent Function

Create a table listing key points, including the x-intercept, that are located between the two vertical asymptotes at

Graph Horizontal Dilations of the Tangent Function

Sketch the curve through the indicated key points for

the function. Then sketch one cycle to the left on

and one cycle to the right on

.

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