Accelerated Math III

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Accelerated Math III

• Monday, November 1
• Why do we graph trig functions?

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(No Transcript)
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One Minute Question

• If
• And a is the amplitude of f(x) and p is the
  period of f(x) ,
• Write the ordered pair (a, p).

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Homework?

• Review from yesterday?
• Questions?

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2nd One-Minute Question

• Write an equation of the sinusoidal curve on the
  screen.
• (Note There are no degree symbols on the
  y-axis.)

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So, When Do We See Sinusoidal Functions??
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One example

• A water wheel 14 feet in diameter is rotating
  counterclockwise. You start a stopwatch and
  observe a point P on the rim of the wheel. At t
  2 seconds, P is at its highest, 13 feet above
  the water. At t 7 seconds, P is at its maximum
  depth below the water.

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What Do You Know???
What Would You Like To Know???
How Can We Find It???
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One example

• A water wheel 14 feet in diameter is rotating
  counterclockwise. You start a stopwatch and
  observe a point P on the rim of the wheel. At t
  2 seconds, P is at its highest, 13 feet above
  the water. At t 7 seconds, P is at its maximum
  depth below the water.

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My Questions

• . What is an equation of Ps motion?
• 2. Where is P at time 6 seconds?
• At what time does point
• P first emerge from
• the water?

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Answers

• . Y 7cos (p/5(x 2)) 6
• 2 . At time 6 seconds, P is.3369 above
• the water.
• . The wheel first emerges
• from the water at
• t 7.861 seconds.

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A Deer Problem

• To avoid a hunter a deer runs in a sinusoidal
  path that crosses a stream. At time 2 sec.,
  the deer is 30 feet to the north of the stream
  and at time 20 sec., the deer is 10 feet to the
  south of the stream. If these are maximum
  distances from the stream that runs east-west,
  write an equation of the deers path.

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Extensions

• . Where is the deer at t 0 seconds?
• . Where is the deer at t 13 seconds?
• . When does the deer first cross the stream?

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Answers

• An equation is
• y 20cos((p/18)(x 2)) 10
• . At t 0 seconds, the deer is 28.79 north of
  the stream.
• . At t 13 seconds, he is 3.16 north of the
  stream.

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Answers

• 3. Suggestions?

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Homework

• In the new Foerster Book, read page 319 321 and
  work problems 1 13 starting on page 321.

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Answers

• To find where he crosses the stream
  algebraically, let
• 20cos((p/18)(x 2)) 10 0
• So 20cos((p/18)(x 2)) -10
• cos((p/18)(x 2)) -1/2
• cos-1(cos((p/18)(x 2)) cos-1(-1/2)
• (p/18)(x 2) 2p/3 2pk
• x 2 12 36k Why is 36 right?
• X 14 36k or x -10 36k so
• X 14, 26, 50 so at t 14, t 26 and t 50,
  the deer crosses the stream.