Download Honors Algebra 2: Chapter 8 Review

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Honors Algebra 2: Chapter 8 Review
1.
(a) Derive the Law of Sines. (One proportion is sufficient)
(b) Derive the Law of Cosines. (One proportion is sufficient)
2.
Express in complex trigonometric form:
z= -3 + 4i
3. A rhombus has sides of length 100 cm, and the angle at one of the vertices is 70. Approximate
the length of each diagonal to the nearest hundredth of a centimeter.
4.
Express in standard complex form:
4(cos
11
11
+ i sin
)
6
6
5. Scott and David are members of a surveying crew that is given the job of finding the height of
Mt. Seaholm (See the diagram below. Drawing not to scale. From a point on level ground,
David measures the angle of elevation to the top of the mountain at 22 . Scott is 710 meters
closer to the mountain along the same line. He measures the angle of elevation to the top of the
mountain at 46 . How high is the mountain?
46
22
Scott
710m
David
6. The cruise ship S.S. Seaholm carrying all of the Honors Algebra 2 students on a vacation as a
reward for all of their hard work, travels 80 miles due east, Captain Guinn then adjusts its course
15 northward. After traveling 100 miles in that direction, how far is the ship from its point of
departure (Linear distance from A to B)? What is the area of the triangle in the drawing? Round
your answers to the nearest tenth.
B
100 miles
15
A
80 miles
7. a) What is the value of all the angles?
5
12
b) Calculate the area of the triangle using Heron’s Formula
c) Calculate the area of the triangle using the Law of Sines
10
8. Evaluate using DeMoivre’s Theorem to be eligible for any amount of credit. Use of another
method is not permitted. You may leave the answer in simplified radical form.
 3  4i 
9.
Find: z1 z2 and
Z1= 3(cos
7
z1
z2


+ i sin )
3
3
10. Solve for the Five Fifth Roots:
Z2 = 2(cos
x5  32  0


+ i sin )
4
4
11. What is the value of x?
17
18
x
25
12. What is the value of  ?
5
12

10
13. To approximate the length of Lake Seaholm, Molly starts at one end of the lake and
walks 245 meters as shown below in the drawing. She then turns 70º and walks 270
meters until she arrives at the other end of the lake. Approximately how long is the lake?
70
270 meters
245 meters
14. a) What is the value of all the angles?
6
13
b) Calculate the area of the triangle
11

15. Find: 2  2 3i

6
16. Find the three cube roots of: 2  2i
17. Express is standard form: (a+bi):
 

 
 2  cos 4  i sin 4  

 
5