Do Now:

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Do Now

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Algebra II Honors

• 4.5 and 4.6 Graphing Trig Functions

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Function table

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

x -2 -1 0 1 2
f(x)
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Function Table

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

x 0
sin(x)
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Graph y sin(x)
x 0
sin(x) 0 1 0 -1 0










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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.)

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Function Table

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

x 0
cos(x)
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Graph y cos(x)
x 0
cos(x) 1 0 -1 0 1










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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.)

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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 .

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Find the period and amplitude of the graph.

• 1.)
• 2.)
• 3.)

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Sketch one period of the graph.




















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Sketch one period of the graph.




















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Sketch one period of the graph.




















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Closing

• What are the steps for graphing a sin and cosine
  function?

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Homework

• Packet
• 1-14 even 39, 40,45, 46, 50, 51

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Function Table

• Lets try the tangent function.

x
tan(x)
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Graph of y tan x

• Tangent graph is periodic (period for y tan x
  is ).

• Vertical asymptotes

• X-intercepts

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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 .

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Sketch one period of the graph.




















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table

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

x
tan(x)
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Graph of y cot x

• Cotangent graph is periodic (period for y cot x
  is ).

• Vertical asymptotes

• X-intercepts

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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 .

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Sketch one period of the graph.










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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.

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Sketch one period of the graph.




















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Sketch one period of the graph.




















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Homework

• Worksheet
• 9 29 odd