Chapter 6 Periodic Functions

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Chapter 6Periodic Functions 6.1 The Sine and
Cosine Functions 6.2 Circular Functions and
their Graphs 6.3 Sinusoidal Models 6.4
Inverse Circular (Trigonometric) Functions
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Average Daily High Temperatures in New York City
H(t) 24sin(0.0172(t-120)) 62
On what days was the average daily high
temperature equal to 50 degrees?
50 24sin(0.0172(t-120)) 62
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Inverse Trigonometric Functions
solve sin(t) 1
solve sin(t) 1/2
solve sin(t) -v2/2
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Inverse Trigonometric Functions
solve sin(t) 1/3
t sin-1(1/3)ort arcsin(1/3)
t .34calculator
solve sin(t) -1/3
t 3.14 .34 3.44t 6.28 - .34 5.94unit
circle symmetry
t 3.14 - .34 2.80unit circle symmetry
t .34 2kp t 2.80 2kp
t 3.44 2kp t 5.94 2kp
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Inverse Sine Function
y sin-1(x) or y arcsin(x) means sin(y)
x and p/2 y p/2
arc between p/2 and p/2
number between -1 and 1
sin-1(x)
sin-1(-1/2)
sin-1(0)
otherwise calculator
sin-1(v3/2)
sin-1(1)
sin-1(-v2/2)
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Inverse Sine Function
y sin-1(x) or y arcsin(x) means sin(y)
x and p/2 y p/2
ysin(x)
yarcsin(x)
ySin(x)
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Inverse Cosine Function
y cos-1(x) or y arccos(x) means cos(y)
x and 0 y p
ycos(x)
yarccos(x)
yCos(x)
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Inverse Tangent Function
y tan-1(x) or y arctan(x) means tan(y)
x and p/2 lt y lt p/2
ytan(x)
yarctan(x)
yTan(x)
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More Practice
Page330 53,55,63, 65
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More Practice
Page330 63 (check)
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More Practice
Page330 65 (check)
14sin(Pi(t2.5)/5) 0
12
50 24sin(0.0172(t-120)) 62
7p/6 0.0172(t-120)
(1/0.0172)(7p/6) t-120
-12 24sin(0.0172(t-120))
(1/0.0172)(7p/6) 120 t
-12/24 sin(0.0172(t-120))
333 t
-1/2 sin(0.0172(t-120))
arcsin(-1/2) 0.0172(t-120)
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50 24sin(0.0172(t-120)) 62
-p/6 0.0172(t-120)
(1/0.0172)(-p/6) t-120
-12 24sin(0.0172(t-120))
(1/0.0172)(-p/6) 120 t
-12/24 sin(0.0172(t-120))
90 t
-1/2 sin(0.0172(t-120))
arcsin(-1/2) 0.0172(t-120)
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Homework
Page330 53-70 TURN IN 54, 56, 58, 66
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FINAL EXAM - REVIEW

• TRIG FUNCTIONS
• Basic evaluations (p/6, p/4, p/3, p/2, p )
• Given info to formula to graph.
• Picture to info to formula
• Given sin(t), determine cos(t), tan(t), cot(t),
  sec(t) and csc(t).
• Use inverse trig ideas to solve a trig equation

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FINAL EXAM - REVIEW

• EXAM 2
• Find a shifted exponential formula
• Determine instantaneous rate of change for
  logistic model
• 3) Find and interpret vertex in context.
• Use logarithms to solve an exponential equation.
• Find polynomial formula from zeroes and y
  intercept.

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FINAL EXAM - REVIEW

• EXAM 1
• Identify formulas to match graphs.
• Determine an inverse function.
• 3) Determine a linear model in context.
• Determine a basic exponential model in context.
• Determine a linear model from two points.