6'3 Trigonometric Functions of Real Numbers Periodic Functions Graphs

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6.3 Trigonometric Functions of Real Numbers
Periodic Functions Graphs
Mrs. Kessler
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6.3 Graphs of the Sine and Cosine Functions
Mrs. Kessler
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y
x
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?
?/2
2?
3?/2
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Unwrapping of the Sine Function
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Characteristics of the Sine Function
1. The domain is the set of all real numbers.
2. The range consists of all real numbers from -1
to 1, inclusive.
3. The sine function is an odd function
(symmetric with respect to the origin).
4.
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Characteristics of the Sine Function
5.
6.
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Paris Average Temperatures
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The Graph of the Cosine
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The Graph of y cos x
y
x
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Every point on the unit circle is in the form of
(x, y) and at the same time in the form of (cos
?, sin ?)
x-intercepts are ODD ?/2's
max's at EVEN ?'s
?
?/2
2?
3?/2
mins's at ODD ?'s
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(0, 1)
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(No Transcript)
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Characteristics of the Cosine Function
1. The domain is the set of all real numbers.
2. The range consists of all real numbers from
-1 to 1, inclusive.
3. The cosine function is an even function
(symmetric with respect to the y-axis).
4.
5.
6. The maximum value is 1 and occurs a -4?, -2?,
0, 2?, 4?
7. The minimum value is -1 and occurs a -3?, -?,
?, 3?
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6.3 Graphs of The Other Trigonometric Functions
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Values of y tan x
y
x
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Tangent Function (contd)
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Graph of the Tangent Function

• Is the tangent function is odd or even or
  neither?

The graph of y tan xis symmetric with respect
tothe origin.
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Graph of the Tangent Function

• The domain is ____________________________________
  __
• The range is ______________
• The tangent is odd even or neither.
• The period is __________________
• The y intercept is ____________________
• The x intercepts occur at _______________________
  ______________________
• Determine a formula to describe this. __________
• Is there a maximum? ______________
• Is there a minimum? _______________
• The asymptotes occur at ________________________

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Tangent Function (contd)

• The values of tan x near x p/2 require special
  attention.

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Tangent Function (contd)
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Summary of Trig Functions
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Cotangent Function
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Cotangent Function
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y cot (x)

• The domain is _____________________________ __
• The range is ______________
• The cotangent is odd even or neither.
• The period is __________________
• The y intercept is ____________________
• The x intercepts occur at _______________________
  ______________________
• Determine a formula to describe this. __________
• Is there a maximum? ______________
• Is there a minimum? _______________
• The asymptotes occur at ________________________
• Determine a formula to describe this.
  ________________

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(No Transcript)
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• The secant function

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The secant
y cos(x)
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Secant Function
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Secant Function
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y sec(x)

• The domain is _____________________________ __
• The range is ______________
• The secant is odd even or neither.
• The period is __________________
• The y intercept is ____________________
• The x intercepts occur at _______________________
  ______________________
• Determine a formula to describe this. __________
• Is there a maximum? ______________
• Is there a minimum? _______________
• The asymptotes occur at ________________________
• Determine a formula to describe this.
  ________________

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• The cosecant function

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The cosecant function
y sin(x)
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Cosecant Function
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Cosecant Function
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y csc (x)

• The domain is ____________________________________
  __
• The range is ______________
• The cosecant is odd even or neither.
• The period is __________________
• The y intercept is ____________________
• The x intercepts occur at _______________________
  ______________________
• Determine a formula to describe this. __________
• Is there a maximum? ______________
• Is there a minimum? _______________
• The asymptotes occur at ________________________
• Determine a formula to describe this.
  ________________

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Summary Part 2