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Do Now:

Do Now:. Algebra II Honors. 4.5 and 4.6: Graphing Trig Functions. Function table:. When you first started graphing linear functions you may recall having used the following table to graph. Function Table:.

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Do Now:

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  1. Do Now:

  2. Algebra II Honors 4.5 and 4.6: Graphing Trig Functions

  3. Function table: • When you first started graphing linear functions you may recall having used the following table to graph.

  4. Function Table: • We will still pick convenient x values. Our values will be in radians. Lets try the sine function first.

  5. Graph y = sin(x):

  6. Graph of y = sin x • Sine graph is periodic (period for y = sin x is ). • Five Key Points: Intercepts, Max, and Min. • Amplitude = half the distance bet. the max. and min. (amplitude for y = sin x is 1.)

  7. Function Table: • We will still pick convenient x values. Our values will be in radians. Lets try the sine function first.

  8. Graph y = cos(x):

  9. Graph of y = cos x • Cosine graph is periodic (period for y = cos x is ). • Five Key Points: Intercepts, Max, and Min. • Amplitude = half the distance bet. the max. and min. (amplitude for y = cos x is 1.)

  10. Graphing: • Amplitude = • Period = • Divide the period by 4 to get four equal subintervals. • Phase Shift : solve equations and . • This will give you the left and right endpoints of a period. • Vertical Shift = The graph of is a reflection in the x-axis of .

  11. Find the period and amplitude of the graph. 1.) 2.) 3.)

  12. Sketch one period of the graph.

  13. Sketch one period of the graph.

  14. Sketch one period of the graph.

  15. Closing: • What are the steps for graphing a sin and cosine function?

  16. Homework: • Packet • 1-14 even; 39, 40,45, 46, 50, 51

  17. Function Table: Lets try the tangent function.

  18. Graph of y = tan x • Vertical asymptotes = • X-intercepts = Tangent graph is periodic (period for y = tan x is ).

  19. Graphing: Asymptotes = solve equations and . X-intercept: half way between asymptotes. Period = distance between two consecutive asymptotes. The graph of is a reflection in the y-axis of .

  20. Sketch one period of the graph.

  21. table: Fill in the table for cot(x) and compare it to tan(x).

  22. Graph of y = cot x • Vertical asymptotes = • X-intercepts = Cotangent graph is periodic (period for y = cot x is ).

  23. Graphing: Asymptotes = solve equations and . X-intercept: half way between asymptotes. Period = distance between two consecutive asymptotes. The graph of is a reflection in the y-axis of .

  24. Sketch one period of the graph.

  25. Graphing Cosecant and Secant • Cosecant: graph sine first. • Where sin x = 0, csc x has a vertical asymptote. • Secant: graph cosine first. • Where cos x = 0, sec x has a vertical asymptote.

  26. Sketch one period of the graph.

  27. Sketch one period of the graph.

  28. Homework: • Worksheet • 9 – 29 odd

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