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Accelerated Math III

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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. – PowerPoint PPT presentation

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Title: Accelerated Math III


1
Accelerated Math III
  • Thursday, October 21
  • Why do we graph trig functions?

2
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).

3
Homework?
  • Review from yesterday?
  • Questions?

4
2nd One-Minute Question
  • Write an equation of the sinusoidal curve on the
    screen.
  • (Note There are no degree symbols on the
    y-axis.)

5
10 Question Quiz?
6
So, When Do We See Sinusoidal Functions??
7
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.

8
What Do You Know???
What Would You Like To Know???
How Can We Find It???
9
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.

10
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?

11
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.

12
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.

13
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?

14
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.

15
Answers
  • 3. Suggestions?

16
Homework
  • Page 121 1, 5, 11, 15, 19, 23, 25 28, 33
    36
  • Page 132 Q1 Q7 and 1a-d, 2a-c, and 3a-c

17
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.
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