Post1330_section5o3b

Post1330_section5o3b - Section 5.3b Graphs of the Tangent...

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Section 5.3b – Graphs of the Tangent and Cotangent Functions 1 Section 5.3b Graphs of the Tangent and Cotangent Functions Recall: sin tan cos x x x = so where cos 0 x = , tan x has an asymptote and where sin 0 x = , tan x has an x - intercept. Tangent: ( ) tan f x x = How to graph tan( ) y A Bx C = - : 1. The period is given by B π . Find two consecutive asymptotes by setting B x – C equal to 2 - and 2 and then solve for x . 2. Find an x -intercept by taking the average of the two points on the x -axis where consecutive asymptotes pass. 3. Find the points on the graph ¼ and ¾ of the way between the consecutive asymptotes. The y -coordinates of these points are –A and A. 1 -1 2 2 - - 3 2 3 2 - Period: Vertical Asymptote: 2 k x = , k is an odd integer. x -intercepts: k , k is an integer. y -intercept: (0, 0) Domain: 2 k x , k is an odd integer. Range: ) , ( -∞

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2 Example 1: Describe the transformations of 3 ) 5 tan( ) ( - - = x x f . Example 2:
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This note was uploaded on 02/20/2012 for the course MATH 1330 taught by Professor Staff during the Fall '08 term at University of Houston.

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Post1330_section5o3b - Section 5.3b Graphs of the Tangent...

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