Download PC 4.4-4.6 Review WS 4 pages

Review for Quiz 4.4-4.6
Name: __________________
Class Period: _____________
For questions #1-6, sketch at least 2 periods.


1. y  3sin  3x 

x 
  1
4 3
2. y  2cos 

2
Amplitude:
Phase Shift:
Amplitude:
Phase Shift:
Period:
Vertical Shift:
Period:
Vertical Shift:


3. y  3tan x
4. y  0.5cot  2 x 
Period:
Period:
Vertical Asymptotes:
Vertical Asymptotes:


4
x

   1
3

5. y  csc x  3
6. y  sec 
Period:
Period:
Vertical Asymptotes:
Vertical Asymptotes:
For problems 7-21 find the exact value of the expression, if it exists.

7. arcsin  


3

2 
10. sin(cos 1 x)


sin 1  cos 
3

13.


16. cot  sin 1
2 

9 
19. tan (sin−1 x)
 1
 2
9. tan 1
11. tan 
 3 

 2 
12. cos 1  cos
1
14. cos  tan 0 
1

tan  arcsin1  arccos 
2

15.
8. cos 1   


17. tan  arccos
1
20. arcsin (− 2)
3
3


2 

5 

3 

4 
 3 
 4 
1
18. cos  tan    

21. sin (arctan −
√3
)
3
22. Write a sinusoidal function with the given amplitude, period, phase shift, and vertical shift.
𝜋
Cosine function; Amplitude=15, period = 4π, phase shift = 3 , vertical shift = -7
23. LEAF A leaf floats on the water bobbing up and down. The distance between its highest and lower points is 4 cm. It
moves from its highest point down to its lowers point and back up to its highest point every 10 seconds. Write a cosine
function that models the movement of the leaf in relationship to the equilibrium point.
24. FERRIS WHEEL Noah and Ali’s Ferris wheel has a 55ft radius. This giant Ferris wheel makes one complete
rotation every 16 minutes. If your seat, on the perimeter of the wheel, reaches a maximum height of 111 ft from the
ground 9 min after the wheel begins rotating:
a. Sketch one cycle of your seat’s height on the ferris wheel as function of time.
a. Find an equation that models the height in feet, h, of the given seat as a function of time in minutes, t.
c. After you start timing, when do you first reach the bottom of the Ferris wheel?
d. If the maximum height was actually 120ft, what would the new equation be?
25. SWING Marsha is pushing her brother Bobby on a rope swing over a creek. When she starts the swing, he is 7 feet
over land away from the edge of the creek. After 2 seconds, Bobby is 11 feet over the water past the edge of the creek.
Assume that the distance from the edge of the creek varies sinusoidally with time and that the distance y is positive
when Bobby is over the water and negative when he is over land. Write a trigonometric function that models the
distance Bobby is from the edge of the creek at time t seconds.
26. EYESIGHT The observation deck of the Space Needle in Seattle, Washington, is 526 feet above the ground. A sixfoot-tall man is watching a car on the street below. Let d represent the distance from the Space Needle to the car and θ
the angle of depression. Write d as a function of θ.
27. AMUSEMENT PARKS The Space Shot is a ride at an amusement park that propels passengers straight into the air.
A spectator is standing 20 meters away from the ride. Let d be the distance from the spectator to the passengers on the ride
from their original starting position and θ be the angle of elevation to the passengers from the spectator.
a. Write d as a function of θ.
b. Graph the function on the interval 0° ≤ θ < 90°.
c. Approximate how far are the passengers from the spectator when the angle of elevation is 55°.
28. PROJECTION A teacher is projecting a graph from an overhead projector onto screen in a lecture hall as shown.
a. Write a function modeling the maximum projecting angle θ in terms of d.
b. Use a graphing calculator to determine the distance for the maximum projecting angle.
29. VIDEO At a swim meet, a parent is videotaping his son from a seat in the stands that is 20 meters past the starting line
and 8 meters away from his son’s lane as shown. Let x represent the distance the son has swam.
a. Write x as a function of θ.
b. What angle does the parent have the camera at when the race is just starting?
c. What angle does the parent have the camera at when the son has swam 25 meters?
d. Explain the differences in your answers from parts b and c.