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Section 4.6. Graphs of Other Trigonometric Functions What you should learn Sketch the graphs of tangent functions. Sketch the graphs of cotangent functions. Sketch the graphs of secant and cosecant functions.

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Problem of the Day

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Graph of the Tangent Function y = tan x Recall that the tangent function is odd, thus tan (-x) = -tan x. Therefore, the graph of y = tan x is symmetric with respect to the origin.

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Transforming a Tangent Function y = a tan (bx - c) Two consecutive vertical asymptotes can be found by solving the equations bx – c = - π/2 and bx – c = π/2 The period of the function y = a tan (bx - c) is the distance between two consecutive vertical asymptotes. The midpoint between two vertical asymptotes is an x-intercept of the graph. The amplitude of the tangent function is undefined.

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x-π-π0π tan x/2Und.01Und. Example 1. Sketching the Graph of a Tangent Function

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x0 -3 tan2x Und.30-3Und. Example 2. Sketching the Graph of a Tangent Function

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Problem of the Day

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Graph of the Cotangent Function The graph of the cotangent function is similar to the graph of the tangent function. It has a period of π. Since, The cotangent function has vertical asymptotes when sin x is zero, which occurs at x = nπ, where n is an integer

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Compare and Contrast Tangent and Cotangent

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Graph of the Cotangent Function Two consecutive vertical asymptotes can be found by solving the equations bx – c = 0 and bx – c = π

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Example 3. Sketching the Graph of a Cotangent Function x03π3π 2 cot x/3Und.20-2Und.

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Graphs of the Reciprocal Functions

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Sketch the graph of: Graph of the Cosecant Function

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Sketch the graph of: y = sec 2x Graph of the Secant Function

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Assignment 4-6 4.6 Exercises p. 339 1-6 all p. 368 141-144 all

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