Transcript PCH Notes 4.5dx

Date:
4.5(d) Notes: Modeling Periodic Behavior
Lesson Objective: To find sine and cosine
functions.
CCSS: F-TF Extend the domain of trigonometric
functions using the unit circle.
You will need: graphing calculator
Lesson 1: Using a Graph to Find an Equation
Find an equation of the form y = A sin Bx that
produces the graph shown in the figure.
Lesson 2: Finding an Equation from Data
A region that is 30° north of the Equator averages a minimum of 10 hours of daylight in December. Hours of daylight are at a maximum of
14 hours in June. Let x represent the month of
the year, with 1 representing January, etc. If y
represents the number of hours of daylight in
month, x, use a sine function of the form y = A
sin(Bx – C) + D to model the hours of daylight.
Graph the function.
Lesson 2: Finding an Equation from Data
A region that is 30° north of the Equator averages a minimum of 10 hours of daylight in December. Hours of daylight are at a maximum of
14 hours in June. Let x represent the month of
the year, with 1 representing January, etc. If y
represents the number of hours of daylight in
month, x, use a sine function of the form y = A
sin(Bx – C) + D to model the hours of daylight.
Graph the function.
Min = 10 hrs in Dec., Max = 14 hrs in June
January = 1, Period = 2(Dec. – June) = 2(6) = 12
Lesson 2: Finding an Equation from Data
Min = 10 hrs in Dec., Max = 14 hrs in June
January = 1, Period = 2(Dec. – June) = 2(6) = 12
y = number of hours of daylight in month, x
Lesson 2: Finding an Equation from Data
D = Max + Min =
2
|A| = Max – Min =
2
Phase Shift = C
B
Interval = Period =
4
Period = 2π
B
Lesson 3: More Modeling
The depth of water at a boat dock varies with
the tides. The depth is 5’ at low tide and 13’ at
high tide. On a certain day, low tide is at 4 AM
and high tide is at 10 AM. If y represents the
depth of the water, in feet, x hours after midnight, use a sine function of the form y = A
sin(Bx – C) + D to model the water’s depth.
Graph the function.
Lesson 3: More Modeling
The depth of water at a boat dock varies with
the tides. The depth is 5’ at low tide and 13’ at
high tide. On a certain day, low tide is at 4 AM
and high tide is at 10 AM. If y represents the
depth of the water, in feet, x hours after midnight, use a sine function of the form y = A
sin(Bx – C) + D to model the water’s depth.
Graph the function.
The depth is 5’ at low tide and 13’ at high tide.
Low tide is at 4 AM and high tide is at 10 AM.
Period = 2(10 – 4) = 12
Lesson 3: More Modeling
The depth is 5’ at low tide and 13’ at high tide.
Low tide is at 4 AM and high tide is at 10 AM.
Period = 2(10 – 4) = 12
Lesson 3: More Modeling
D = Max + Min =
2
|A| = Max – Min =
2
Phase Shift = C
B
Interval = Period =
4
Period = 2π
B
4.5(d): Do I Get It? Yes or No
1. Find the equation for the graph.
4.5(d): Do I Get It? Yes or No
4.5(d): Do I Get It? Yes or No
3. Throughout the day, the depth of water at
the end of a dock in Bar Harbor, Maine varies
with the tides. The table shows the depths (in
feet) at various times during the morning.
a. Use a trigonometric function to model the
data.
b. Find the depths at 9 A.M. and 3 P.M.
c. A boat needs at least 10 feet of water to
moor at the dock. During what times in the
afternoon can it safely dock?
4.5(d): Do I Get It? Yes or No
a. Use a trigonometric function to model the
data.
4.5(d): Do I Get It? Yes or No
b. Find the depths at 9 A.M. and 3 P.M.
c. A boat needs at least 10 feet of water to
moor at the dock. During what times in the
afternoon can it safely dock?