Pre-Calc 4.5-4.8 Review
Use at least 3 decimal places, watch conversions!
Name: _______________________
Problems # 1-7, Word Problems.
1. Adrian is in an airplane (commercial jet) 7 miles above the ground. He looks out of the window and in the
distance, sees a lake. At one end of the lake he sees a dock at an angle of depression of 27, and at the other
side of the lake he sees the marina at 72. The length of the lake can be calculated between the dock and
marina. If the plane, dock, and marina are in a straight line, how long is the lake?
ANS _____________________feet
ANS_____________________ miles
2. A ship, captained by Jimmy, leaves the port at a constant rate of 40 miles per hour at noon and has a bearing
of S12 E after sailing for 8 hours the ship changes course by a ninety degree angle for a new bearing of
N 78 E and sails for another 3 hours to avoid a storm. The ship then has engine failure and calls for the coast
guard. In relationship to the port, what bearing should the coast guard take to Jimmy, and how far will they
need to travel to get to the disabled ship?
ANS _____________________miles
Bearing ANS________________
3. You are standing top of a stapler with no shoes on. I don’t know why, but it is obvious why you aren’t
wearing any shoes. From your line of sight you are looking down 86 to see the front of the stapler and, in
turning around, you look down 89 to see the back of it. Your height (bottom of your feet to eyes) is 5 ft 6
inches. Find the length of the stapler in inches.
ANS ________in.
4. You are watching a jet (with Adrian inside) flying overhead. You know the exact top speed of this jet is 855
m.p.h. because you are nerd. You first view the angle of elevation of the plane to be 26 . Within 32 seconds it
is almost directly over top of you at an angle of 83 . Assuming the jet is at its top speed…how high is the jet
flying?
ANS _____________________feet
ANS_____________________ miles
5. From Detroit Rock City to New New York, Ashley flies a plane 650 miles at a bearing of N 48 o E. From
New New York to Gotham City, she flies 810 miles at a bearing of S 65o E. Find the distance from Detroit
Rock City to Gotham City and the bearing from Detroit Rock City to Gotham City.
ANS _____________________ miles
Bearing_____________________
6. The height of a cell phone tower is 70 meters. It casts a shadow of 30 meters. Find the angle of elevation of
the sun.
ANS _____________________
7. Hailey tosses a Frisbee and it lands at the edge of the roof of the school. When she is 25 feet from the base
of the building, the angle of elevation to the Frisbee is 19o. How high off the ground is the Frisbee?
ANS _____________________ feet
Problems # 8-15, Graph ONE period of the following..label everything! (including the appropriate # of
pts on x- and y- axis as determined in class) NO decimals are accepted on this section.
8.
𝑦 = 2 csc(3𝑥 − 𝜋) − 1
AMP:
PERIOD:
HOR Start:
End:
VER SHIFT:
Reflect?
𝜋
9. 𝑦 = tan (3𝜋𝑥 − 4 ) + 1
AMP:
PERIOD:
HOR Start:
End:
VER SHIFT:
Reflect?
10. 𝑦 = −cot(𝑥 + 2𝜋) − 3
AMP:
PERIOD:
HOR Start:
End:
VER SHIFT:
Reflect?
11. 𝑦 = − sec(13𝜋 + 19𝑥) + 3
AMP:
PERIOD:
HOR Start:
End:
VER SHIFT:
Reflect?
12.
𝑦 = − cos(𝜋𝑥 − 𝜋) + 2
AMP:
PERIOD:
HOR Start:
End:
VER SHIFT:
Reflect?
𝜋
13. 𝑦 = −2sin (3𝑥 − 4 ) + 1
AMP:
PERIOD:
HOR Start:
End:
VER SHIFT:
Reflect?
14. 𝑦 = −tan(7𝑥 + 2𝜋) − 3
AMP:
PERIOD:
HOR Start:
End:
VER SHIFT:
Reflect?
15. 𝑦 = sec(9𝑥) − 1
AMP:
PERIOD:
HOR Start:
End:
VER SHIFT:
Reflect?
Refer to triangle for problems 16 and 17
Solve for all parts: Decimals are acceptable for answers in this section.
16.
A. 63
a.
B.
C.
17.
A.
a. 65
b.
B.
b.
c. 56
C.
c. 100
Problems # 18-20, Find the EXACT algebraic expression.
18. cos⁡(𝑎𝑟𝑐𝑡𝑎𝑛
√𝑥+𝑡
)
𝑦
6
19. sec⁡(arcsin (− 11))
20. csc⁡(𝑎𝑟𝑐𝑐𝑜𝑠√𝑥 − 7)
Problems # 21-25, Simplify the expression.
21. arcsin(sin(4.235))
22. sin(arcsin(0.567))
23. arccos(cos(5.7))
24. arctan(tan(2.8))
25. tan(arctan(2.91))
Plus, study ALL homework from sections 4.5-4.8. Focus on all word problems!!