Download 13.5+13.6 Review - Issaquah Connect

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13.5+13.6 Review
1. The number of hours of daylight on any day of the year in Philadelphia, Pennsylvania, is modeled using the
2
equation y  12  2.5sin
 x  80  where x represents the day number (with January 1 as day 1). This
365
equation assumes a 365-day year (not a leap year).
a. Interpret the meaning of the point y (0)  12 in the context of this problem.
b. What is the minimum number of hours of daylight in Philadelphia?
c. Find the number of hours of daylight in the longest day of the year (the summer solstice).
d. Find the nearest two whole days when the number of hours of daylight is closest to 13. (C)
2. During an earthquake, the rolling of the ground can be modeled by a sinusoidal equation. You are standing on
a sidewalk that is 8.5 inches above the road. When the earthquake begins your height above the road
fluctuates a total amount of 5 inches. You realize at 4 seconds you are at your lowest point and return to that
height every 7 s.
a. What is your vertical dilation/amplitude?
b. What is your vertical translation/sinusoidal axis (midline)?
c. What is your period?
d. If your equation is written using cosine, what is your horizontal translation/phase shift?
e. Write an equation that models your height during the earthquake.

 t  2   26.5 models the average daily temperature (in degrees Fahrenheit) in
6
Fairbanks, Alaska. Time t is measured in months, with t  0 representing January 1.
a. What is the maximum temperature and during what month(s) does it occur?
3. The equation F (t )  37 sin
b. What is the minimum temperature and during what month(s) does it occur?
c. How many months during the year is the temperature 26.5 ?
4. Evaluate, giving exact values (Hint: Remember your unit circle!)

5
a. tan
b. cot
3
6
d. csc
4
3
5. Given tan   
e. cot 
c. sec
f.
csc

4
7
6
7
and 180    360 , find the other five trigonometric ratios.
24
6. Suppose sin x  0.8 .
a. Using a Pythagorean Identity involving sin x and cos x , find all possible values for cos x .
b. Find all possible values for x in the domain 0  x  2 .
7. Show that each of the following is a trigonometric identity (remember: rewrite only one side).
a.
 sin   cos  
2
 1  2sin  cos 
c. cot  sin 2   tan  cos 2   0
b.
 sec
d.
 csc  cot   csc  cot    1
2
  tan 2   cos 2   cos 2 