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Graphs of Other Trigonometric Functions. 11-2. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Algebra 2. Holt Algebra 2. Warm Up If sin A = , evaluate. 1 . cos A 2. tan A 3. cot A 4. sec A 5. csc A. Objective.

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11-2

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  1. Graphs of Other Trigonometric Functions 11-2 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 2 Holt Algebra 2

  2. Warm Up If sin A = , evaluate. 1.cos A2. tan A 3. cot A 4. sec A 5. csc A

  3. Objective Recognize and graph trigonometric functions.

  4. The tangent and cotangent functions can be graphed on the coordinate plane. The tangent function is undefined when θ= + n, where n is an integer. The cotangent function is undefined when θ = n. These values are excluded from the domain and are represented by vertical asymptotes on the graph. Because tangent and cotangent have no maximum or minimum values, amplitude is undefined. To graph tangent and cotangent, let the variable x represent the angle θ in standard position.

  5. Like sine and cosine, you can transform the tangent function.

  6. Using f(x) = tan x as a guide, graph Identify the period, g(x) = x-intercepts,and asymptotes. Because b = the period is Example 1: Transforming Tangent Functions Step 1 Identify the period. Step 2 Identify the x-intercepts. The first x-intercept occurs at x = 0. Because the period is 3, the x-intercepts occurs at 3n where n is an integer.

  7. Because b = , the asymptotes occur at Example 1 Continued Step 3 Identify the asymptotes. Step 4 Graph using all of the information about the function.

  8. Because b = the period is Check It Out! Example 1 Using f(x) = tan x as a guide, graph . Identify the period, x-intercepts, and asymptotes. Step 1 Identify the period. Step 2 Identify the x-intercepts. The first x-intercept occurs at x = 0. Because the period is 2, the x-intercepts occur at 2n where n is an integer.

  9. Check It Out! Example 1 Continued Step 3 Identify the asymptotes. Step 4 Graph using all of the information about the function.

  10. Step 1 Identify the period. Because b = 3 the period is The first x-intercept occurs at x = . Because the period is , the x-intercepts occurs at , where n is an integer. Example 2: Graphing the Cotangent Function Using f(x) = cot x as a guide, graph . Identify the period, x-intercepts, and asymptotes. Step 2 Identify the x-intercepts.

  11. Example 2: Graphing the Cotangent Function Step 3 Identify the asymptotes. Because b = 3, the asymptotes occur at Step 4 Graph using all of the information about the function.

  12. Because b = 2 the period is . Step 2 Identify the x-intercepts. The first x-intercept occurs at x = . Because the period is , the x-intercepts occurs at , where n is an integer. Check It Out! Example 2 Using f(x) = cot x as a guide, graph g(x) = –cot2x. Identify the period, x-intercepts, and asymptotes. Step 1 Identify the period.

  13. Because b = 2, the asymptotes occur at x = Check It Out! Example 2 Continued Step 3 Identify the asymptotes. Step 4 Graph using all of the information about the function.

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