1. Accelerated Precalculus
November 8, 2018
Happy Thursday!

2. One-Minute Question
Write the equation of the curve on the board.

3. Homework??
Questions?

4. 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.

5. Extensions . Where is the deer at t = 0 seconds?
. What are the first 3 times at which the deer will cross the stream?

6. 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.

7. 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
arccos(cos((π/18)(x – 2)) = arccos(-1/2)
(π/18)(x – 2) = ±2π/3 + 2πk
x – 2 = ± k **** Why is 36 right?
X = k or x = k so…
X = {14, 26, 50} so at t = 14, t = 26 and t = 50, the deer crosses the stream.

8. Another 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.

9. Questions: . Write an equation of the motion.
. At what time does the wheel first emerge from the water?
. Where is P at time =
6 seconds?

10. Questions: . Y = 7cos (π/5(x – 2)) + 6
. The wheel first emerges from the water at t = seconds.
. At time =
6 seconds,
P is.3369’ above
the water.