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Precalculus Lesson

Precalculus Lesson. 4.6 . Check: p. 326 [Evens] # 12-18, 32-36, 50-54. Warm-up. Graph 2 full periods. Answers. On other sheet. Objective:. Graph sine cosine and tangent functions, and their reciprocals. 4.6 Digital Lesson.

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Precalculus Lesson

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  1. PrecalculusLesson 4.6 Check:p. 326 [Evens] # 12-18, 32-36, 50-54

  2. Warm-up Graph 2 full periods.

  3. Answers On other sheet

  4. Objective: Graph sine cosine and tangent functions, and their reciprocals.

  5. 4.6 Digital Lesson Graphs of Trigonometric Functions Tangent, cotangent, secant, and cosecant

  6. To graph y = tan x, use the identity . y Properties of y = tan x 1. domain : all real x x 4. vertical asymptotes: period: Tangent Function Graph of the Tangent Function At values of x for which cos x = 0, the tangent function is undefined and its graph has vertical asymptotes. 2. range: (–, +) 3. period: 

  7. Example: Find the period and asymptotes and sketch the graph of y x 3. Plot several points in Example: Tangent Function 1. Period of y = tanx is. 2.Find consecutive vertical asymptotesby solving for x: Vertical asymptotes: 4. Sketch one branch and repeat.

  8. y To graph y = cot x, use the identity . Properties of y = cot x x 1. domain : all real x 4. vertical asymptotes: vertical asymptotes Cotangent Function Graph of the Cotangent Function At values of x for which sin x = 0, the cotangent function is undefined and its graph has vertical asymptotes. 2. range: (–, +) 3. period: 

  9. Example 1: Graph a) Consecutive Asymptotes Period: difference between consecutive asymptotes Add or subtract the Period to Consecutive asymptotes to complete 2 periods.

  10. Graph 2 full periods (cycles) • Asymptotes and intercepts.

  11. Example 1:Graph b) Consecutive Asymptotes Period: difference between consecutive asymptotes Add or subtract the Period to Consecutive asymptotes to complete 2 periods.

  12. Graph 2 full periods (cycles) • Asymptotes and intercepts.

  13. The graph y = sec x, use the identity . y Properties of y = sec x 1. domain : all real x x 4. vertical asymptotes: Secant Function Graph of the Secant Function At values of x for which cos x = 0, the secant function is undefined and its graph has vertical asymptotes. 2. range: (–,–1]  [1, +) 3. period: 

  14. To graph y = csc x, use the identity . y Properties of y = csc x 1. domain : all real x x 4. vertical asymptotes: Cosecant Function Graph of the Cosecant Function At values of x for which sin x = 0, the cosecant functionis undefined and its graph has vertical asymptotes. 2. range: (–,–1]  [1, +) 3. period:  where sine is zero.

  15. Example 2 graph a) Table for

  16. Graph 2 full periods (cycles)

  17. Example 2 graph b) Table for

  18. Graph 2 full periods (cycles)

  19. Unit Circle Quiz Tomorrow No Calculator Assignments Classwork: p. 337 # 17, 33, 35 Homework(4.6) (4.6) p. 337 # 16, 18, 22, 34 (4.5) p. 327 # 40, 42, 56, 60

  20. Closure Find the amplitude & period for each. • f(x) = 2cos 4x • G(x) = -5sin 2x • H(x) = tan x • P(x) = 3 cot 2x

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