Download Review Sheet: Study old quizzes and notes as well

Review Sheet: Study old quizzes and notes as well Name:________________________
Integrated IV: High Dive
Date:____________ Period:_______
COMPLETE ALL WORK ON YOUR OWN PAPER PLEASE!!!
1.) Find both the height and the x – coordinate of the diver:
a.) at t = 16 seconds
b.) after the Ferris wheel has turned 206o
c.) at the 8:30 position
2.) Find the percentage of time the diver is above a 30 foot fence.
3.) Sketch the following without a calculator
a.) y = 20 + 40 sin(10x)
b.) y = –25cos(12x) c.) y = 9 – sin(x – 90)
4.) Find a million equations, minimum of 4, for each of the following…
a.)
b.)
c.)
5.) Solve for all values of x between -360o and 360o.
a.) sin x = sin 100o
b.) cos x = -.21
c.) sinx = 1.5
5.5) Provide all expressions using sin and cos between -360o and 360o that is equivalent
to sin 35o.
6.) Find all times when the diver will be 35 feet from the ground algebraically.
7.) The table below lists the average monthly temperatures in degrees Fahrenheit for the
city of Fairbanks, Alaska. The table gives y, the average monthly temperature, as a
function of t, the month, where t = 0 indicates January.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
t
0
1
2
3
4
5
6
7
8
9
10
11
y -11.5 -9.5 0.5 18.0 36.9 53.1 61.3 59.9 48.8 31.7 12.2 -3.3
a.) Find a formula for a function that models the temperature data. Explain how you
found your formula. [NOTE: There are many correct answers]
b.) In the southern hemisphere, the times at which summer and winter occur are reversed,
relative to the northern hemisphere. Modify your formula so that it represents the average
monthly temperature for a southern-hemisphere city whose summer and winter
temperatures are similar to Fairbanks Alasksa.
8.) Find the polar coordinates of the ordered pair (5,8)…and another…and another…
9.) Find the rectangular coordinates of the polar coordinate (115, 115o)
10.) Find the dimensions of the figure below if the area = 75 sq. ft. TRIAL AND ERROR = F
X + 10
X
11.) List all trigonometric identities reviewed throughout the unit. Verify each in terms of
the Ferris Wheel problem.
12.) If cos = .6, use the Pythagorean identity to find the value of sin.
13.) If a point (-4,-5) lies on the terminal side of the angle, find the sine and cosine of
the angle and explain how this fits our extended definition of the sine and cosine
function.
7  2 .) The Rabbit Problem: A rabbit population in a national park rises and falls each
year. It reaches its minimum of 5000 rabbits in January. By July, the population triples
in size. By the following January, the population again falls to 5000 rabbits, completing
the annual cycle. Let the function R be the size of the rabbit population as a function of t,
the number of months since January.
a.) What is the period?
b.) What is the amplitude?
c.) What is the equation of the midline?
d.) Write an equation for R(t) using the sine function.
e.) Graph the function R(t) on your calculator using the appropriate window.
f.) Approximate the population of rabbits on October 15th.
g.) When, approximately, will the population reach 1350 rabbits?
h.) Find R(2). What does R(2) mean in terms of rabbits?
i.) Explain the behavior of the graph over the course of a year. Why would it fluctuate up
and down so much?
A biologist is studying the fox population in the same national park. She finds that F, the
number of foxes in the park, is a function of t, the number of months elapsed since January.
From the data, she came up with the following equation. F (t )  200 sin 30x  6  350
j.)What is the period?
k.)What is the equation of the midline?
l.)What is the amplitude?
m.) By hand (without your graphing calculator!) sketch F(t) over a 12 month time interval.
You can check with your calculator when you are finished.
n.) Over what time interval does the fox population appear to be increasing?
o.)When does the fox population appear to be decreasing?
p.) Over what interval does the fox population appear to be increasing faster and faster?
q.) On what specific date does the fox population appear to be increasing the fastest?
r.) The biologist believes that the park’s rabbit population supplies the fox population
with its principal source of food. Compare the graph of F(t) to R(t). Do these graphs
support her theory? Explain…
15.) Falling objects with initial velocity…don’t forget Days 20 – 25
Phew…I am tired…I am sure you are too. The hard work will pay off on Monday!