PreCalculus
Spring Semester Review 2017
NAME___________________________
PERIOD___________
Write a sine and cosine function for the graph given.
1.


a) ____________________










b) ____________________


2.










a) ____________________









b) ____________________
Graph one complete cycle of the following function.


3. f(x) = -4 cos 2  x   – 1
6

Per: _________
Amp: ________
Hor: _________
Vert: _________
4. Determine the amplitude, period, phase shift, vertical shift, domain, range..
Amplitude
Period
Phase shift
Vertical
shift
Domain
Range
𝜋
𝑦 = 3𝑠𝑖𝑛 (𝑥 − ) + 4
2
𝑦 = −4 cos(2𝑥 + 3𝜋) − 5
Simplify
5. (1 – cosӨ)(1+cosӨ)
6.
tan 2   sec 2 
7.
1  cot  1  cot    csc2 
Using the Sum and Difference Formulas write the expression as a sin, cosine, or tangent of an angle
8. Cos 75°Cos 20° + Sin 75° Sin 20°
9. Sin 30° Cos 75° + Cos 30° Sin 75°
10. Sin 20°Cos 10° + Cos 20°Sin 10°
11. Cos 70°Cos 20° -Sin 70°Sin 20°
12. Sin 20°Cos 80° - Cos 20°Sin 80°
13. Cos 40°Cos 10° + Sin 40°Sin 10°
4
5
14. If the Sin A = 5 and Cos B = 13 , where A and B are acute angles, find the values of:
a) Sin(A+B)
1
b) Sin(A-B)
c) Cos(A+B)
d) Cos(A-B)
2
15. If the Sin A = 2 and Cos B = 3 , where A and B are acute angles, find the values of:
a) Sin(A+B)
b) Sin(A-B)
c) Cos(A+B)
d) Cos(A-B)
Solve each equation for [0, 360°) 𝑎𝑛𝑑 [0,2𝜋) for #16-17.
16. 4 tan 𝜃 + 5 = 1
17. 5 cos 𝑥 + 1 = 4 − cos 𝑥
18. If 𝒂 = 〈2,5〉 𝑎𝑛𝑑 𝒃 = 〈−4, −2〉 find 3a - 4b.
19. Given P = (−3,6) and Q = (2, −3) find magnitude and direction of PQ .
20. George pulls on a rope attached to a boulder at 47° with a force of 72N. Frank pulls on a rope attached to
the same boulder at −32° with a force of 102N. find the magnitude and direction of the resultant force.
21. A golfer hits a ball with an initial velocity of 128 feet per second and at an angle of 42 degrees from the
horizontal.
A. Find when and where the ball will hit the ground.
B. Will the ball clear a fence 100 feet high that is at a distance of 290 feet from the golfer?
C. What is the maximum height of the ball and when does it reach the maximum?
22. Write the following parametric equations as a linear equation by eliminating the parameter.
a)x = 1 + 3t
b) x = 4 + 3t
y=t +4
y = 2 +4t
23. For the following pair of parametric equation: a) Draw the graph and show the orientation. b) Write the
rectangular equation.
x = t2 + 2 and y = 3 – t , for t in (-2, 3)
a)
10
b)
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
-2
-4
-6
-8
-10
4
6
8
10
For each point (r, θ), give rectangular coordinates (x, y). Show your work.
7π 

  10, 
6 
24. 
 3π 
 6, 
25.  4 
For each point (x, y), give two sets of polar coordinates (r, θ), where 0  θ  2π. Show your work.

26.  3 2 , 3


27.  2 ,  6

Convert the equation from rectangular to polar form.
28. x2 + (y + 2)2 = 4
Convert each equation from polar to rectangular form.
29. r = - 3 sin θ
30. r (1  4sin )  5
31. What is the 15th term of the arithmetic sequence a1  5, and d  4?
32. Express the following sum using sigma notation: 8 + 12 + 18 + 27 +…
33. For an arithmetic sequence with a6 = 10 and a62 = 38, what is a28?
34. Find the sum of the first 39 terms of the arithmetic series, -1 + -3 + -5 + -7 …

 2
35. Find the sum of   4  
 3
k 1
k 1
36. What is a converging series? Give an example.
37. What is a divergent series? Give an example.
Sketch a graph of the following:
38. 𝑟 = 4 − 5 cos 𝜃
39. 𝑟 = 3 + 2 sin 𝜃
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
2
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8 10
Determine if a triangle can be formed, if so, solve the triangle?
40. A=470 , b=32 ft, c=19 ft
41. B=1010 , a=10 cm, c=22 cm
42. a=4, b=5, c=8
43. Two markers A and B on the same side of a canyon rim are 80 ft apart, as shown in the figure. A hiker is located
across the rim at point C. A surveyor determines that ∠BAC=700 and ∠ABC=650 . What is the distance between the
hiker and point A? What is the distance between the two canyon rims? (Assume they are parallel)
44. A hot-air balloon is seen over Albuquerque, New Mexico, simultaneously by two observers at points A and B
that are 1.75 mi apart on level ground and in line with the balloon. The angles of elevation are as shown here. How
high above ground is the balloon?
45. A tree is 20 feet tall. Its shadow is currently 35 feet long and the shadow of a shorter tree is 15.5 feet long. How
tall is the shorter tree?
Solve the equations for the interval 0,360  and[0,2𝜋).
46. 2cos x  sec x  1
47. 2cos x  sin2 x  2  0