Trigonometry

1
Trigonometry

• Basic Graphing Terms

2
Amplitude

• the distance from the axis to a high point
• the distance from the axis to a low point
• half the distance from a high point to a low point

3
Standard Form Equation
4
Cycle

• the portion of the curve from one point to where
  the curve starts repeating
• Example As a Ferris Wheel turns, a cycle would
  correspond to one complete revolution.

5
Standard Form Equation
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Period

• the number of degrees/radians
  to complete one cycle

7
Frequency

• the reciprocal of period
• Example The period of a Ferris Wheel is 20
  seconds or 1/3 minute per revolution---gt The
  frequency of the Ferris Wheel is 3 revolutions
  per minute.

8
Find the amplitude period for the graph of each
equation
9
Horizontal Shifts

• Horizontal Shifts do not change the shape of the
  graph, only the position.
• d is the horizontal shift (phase shift)

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Horizontal Shifts

• if d is subtracted, shift right
• if d is added, shift left
• Ex.
• Ex.

11
Vertical Shifts

• Vertical Shifts do not change the shape of the
  graph, only the position.

• c is the vertical shift

• if c is positive, shift up
• if c is negative, shift down

12
Vertical Shifts
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Standard Form Equation
c vertical shift ALWAYS INDICATE
DIRECTION!! a amplitude ( if you take the
absolute value ) b cycles per 2p
p 2p/b d phase shift or horizontal
displacement ALWAYS INDICATE DIRECTION