6 1 a Graphs of Trigonometric Functions Tangent

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Graph of the Tangent Function To graph y = tan x, use the identity

Graph of the Cotangent Function To graph y = cot x, use the identity.

Graph of the Secant Function The graph y = sec x, use the identity

Graph of the Cosecant Function To graph y = csc x, use the identity

Examples: Find ALL the values for Ө for which the equation is true 1.

6. 1 b Homework p. 305; #15, 17, 21 -27, 30 -33, 36, 38,

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6. 1 a Graphs of Trigonometric Functions Tangent, Cotangent, Secant, Cosecant

Graph of the Tangent Function To graph y = tan x, use the identity . At values of x for which cos x = 0, the tangent function is undefined and its graph has vertical asymptotes. y Properties of y = tan x 1. domain : all real x 2. range: (– , + ) 3. period: x 4. vertical asymptotes: period: Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 3

Graph of the Cotangent Function To graph y = cot x, use the identity. At values of x for which sin x = 0, the cotangent function is undefined and its graph has vertical asymptotes. y Properties of y = cot x 1. domain : all real x 2. range: (– , + ) 3. period: 4. vertical asymptotes: x vertical asymptotes Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 4

Graph of the Secant Function The graph y = sec x, use the identity . At values of x for which cos x = 0, the secant function is undefined and its graph has vertical asymptotes. y Properties of y = sec x 1. domain : all real x 2. range: (– , – 1] [1, + ) 3. period: 4. vertical asymptotes: Copyright © by Houghton Mifflin Company, Inc. All rights reserved. x 5

Graph of the Cosecant Function To graph y = csc x, use the identity . At values of x for which sin x = 0, the cosecant function is undefined and its graph has vertical asymptotes. y Properties of y = csc x 1. domain : all real x 2. range: (– , – 1] [1, + ) 3. period: x 4. vertical asymptotes: where sine is zero. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 6

Examples: Find ALL the values for Ө for which the equation is true 1. tan Ө = -1 135° + 180 k° (Where k is an integer) 2. cot Ө = 1 45° + 180 k° (Where k is an integer) Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 7