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Accelerated Math III

Accelerated Math III. Friday, October 21 Why do we graph trig functions?. 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). Homework?. Review from yesterday? Questions?. 2 nd One-Minute Question.

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Accelerated Math III

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  1. Accelerated Math III Friday, 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 P’s motion? 2. Where is P at time = 6 seconds? • At what time does point P first emerge from the water?

  11. Answers: • . Y = 7cos (π/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 deer’s 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((π/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 1:a-d, 2:a-c, and 3:a-c

  17. Answers To find where he crosses the stream algebraically, let 20cos((π/18)(x – 2)) + 10 = 0 • So 20cos((π/18)(x – 2)) = -10 • cos((π/18)(x – 2)) = -1/2 • cos-1(cos((π/18)(x – 2)) = cos-1(-1/2) • (π/18)(x – 2) = ±2π/3 + 2πk • 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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