unit 7 end checkpiont apply trigonometric functions, assignment help

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Unit 7: Trigonometric Functions End Checkpoint Apply
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Unit 7: Trigonometric Functions End Checkpoint Apply
Lesson 4 – 7
Algebra 2
Please complete the following questions. It is important that you show all work you did to solve the
problems when you submit your work. This includes any calculations, diagrams, or graphs that
helped you solve it.
1. OPEN ENDED Write an equation giving the value of the Cosine function for an angle measure in
its domain. Then, write your equation in the form of an inverse function.
2. OPEN ENDED Write the equation of a trigonometric function with a phase shift of -45°. Then
graph the function, and its parent graph.
3. Writing in Math If the formula for the temperature Tin degrees Fahrenheit of a city tmonths into the year is given by T = 50 + 25
sin(67), explain how to find the average temperature and the maximum and minimum predicted over the year.
4. Writing in Math Use the information on page 842 to explain how you can predict the behavior of tides. Explain why certain tidal
characteristics follow the patterns seen in the graph of the sine function.
Your Answer
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intervisualtechnology.us/uploads/PDFs/ebooks/CC%20-%20Algebra%202/CC%20-%20Algebra%202
Furations
842 – 843 / 1100
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New Vocabulary
amplitude
GET READY for the Lesson
The rise and fall of tides can have
great impact on the communities
and ecosystems that depend
upon them. One type of tide is a
semidiurnal tide. This means that
bodies of water, like the Atlantic
Ocean, have two high tides and
two low tides a day. Because
tides are periodic, they behave
the same way each day
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Notice that both the sine and cosine have a mim va
value of -1. The amplitude of the graph of a rodicu
value of half the difference bxtween its maximim value
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So, for both the sine and cosine functions, the mplitude la
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By examining the values for tan in the table, you
function is not defined for 90, 270″…………
graph is separated by vertical asymptotes whose intercepts are the values for
which ytan is not defined
+
Graph Trigonometric Functions The diagram below illustrates the water
level as a function of time for a body of water with semidiurnal tides.
ligh Tide
COncepts
In Motion
Animation
algebra.com
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Review
Vocabulary
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In each cycle of high and low tides, the pattern repeats itself. Recall that
a function whose graph repeats a basic pattern is said to be periodic
To find the period, start from any point on the graph and proceed to the
right until the pallern begins to repeat. The simplest approach is to begin
at the origin. Notice that after about 12 hours the graph begins to repeat
Thus, the period of the function is about 12 hours.
To graph the functions y = sin 8y = cos , or y = tan ,use values of
expressed either in degrees or radians. Ordered pairs for points on these
graphs are of the form (e, sin 8),(C,cost), and (tan), respectively
The period of the tangent function is 180° or 1 radians. Since the tangent
function has no maximum er minimum value, it has no amplitude
Compare the graphs of the secant, cosecant, and cotangent functions to the
graphs of the cosine, sine, and tangent functions, shown below.
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Notice that the period of the servant and consecant functions is 367 or 2t radians
The period of the cotangent is 180° or s radians. Since none of these functions
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