### 7 - Radian Trig Graph Word Problems.notebook

```7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
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7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
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7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
Radian Trig Graph Word Problems
Goal: To solve word problems involving radian trig graph equations that model real­life phenomena. 3
7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
Solving Trigonometric Word Problems using Trig Graphs
MAKE SURE YOUR CALCULATOR IS IN RADIAN 1.) The tide at a boat dock can be modeled by MODE!!!!!!
the equation:
Amplitude = where t is the number of hours past noon and y is the height of the tide in feet
Frequency=
Period=
How many hours between t = 0 and t = 12 is the tide at least 7 feet?
x min
x max
x scl
y min
y max
y scl
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7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
2.) The temperature in Syracuse varies throughout the year. A Sinusoidal equation provides a good model for the average temperature throughout the year. The equation:
represents the average temperature in Syracuse as a function of time, t in months. Note: t = 0 represents January 1st
_____________To the nearest integer What is the average temperature in January?
_____________To the nearest integer What is the average temperature in February
_____________What is the amplitude of the equation?
Nearest whole degree
x min
x max
x scl
y min
y max
y scl
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7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
3.) The occurrence of sunspots during September can be modeled by the equation:
Note: 30 days in September
in which x is the day of the month. What are the maximum number of sunspots that occurred in September?
What are the minimum number of sunspots that occurred in September?
What is the average value of sunspots that occurred in September? Note: (Max + Min)/2 x min
x max
x scl
y min
y max
y scl
Amplitude = Frequency=
Period=
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7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
4.) x min
x max
x scl
y min
y max
y scl
Amplitude = Frequency=
Period=
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7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
5.) A grandfather clock has a pendulum that moves from its central position according to the function Where t represents time in seconds.
How many seconds does it take the clock to complete one full cycle from center to the left then the right and then back to center?
x min
x max
x scl
y min
y max
y scl
Amplitude = Frequency=
Period=
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7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
6.) The depth of the water on the shore of a beach varies as the tide moves in and out. The equation:
models the depth of the water, D(t), in feet and t as time in hours.
a.)_____________What is the amplitude of the equation?
b.)_____________What is the period of the equation?
c.)_____________In how many hours will the tide be at its lowest?
d.)_____________How deep will the water be 2 hours after the high tide?
e.)_____________When will the water be 2 feet deep? Nearest tenth of an hour
x min
x max
x scl
y min
y max
y scl
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7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
Homework: pg. 407­409 #'s 1,2,4,5
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7 ­ Radian Trig Graph Word Problems.notebook
March 14, 2014
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