Download ExamView - Test2.tst

Name: ________________________ Class: ___________________ Date: __________
Test2 (1600 Trigonometry)
Time: 100 minutes
Instructor: Koshal Dahal
SHOW ALL WORK, EVEN FOR MULTIPLE CHOICE QUESTIONS, TO RECEIVE FULL CREDIT.
____
1. Find the degree measure of the angle:
a.
b.
c.
d.
____

15
rad.
27
16
12
6
2. Find sin a and cos  if x = 4, and y = 1.
a.
sin a =
b.
sin a =
c.
sin a =
4
, cos  
17
1
, cos  
17
1
, cos  
17
4
17
1
17
4
17
____
3. The angle of elevation to the top of a particular skyscraper in New York is found to be 12  from the ground at
a distance of 1.3 mi from the base of the building. Using this information, find the height of the skyscraper.
a. 1560 ft
b. 2918 ft
c. 1459 ft
____
4. Find the reference angle for the angle measuring
a.
b.
c.
d.

4
11
15
.
11
4
15
11
4
4
11
1
Name: ________________________
ID: A
____
5. Find the area of an equilateral triangle with sides of length 5.
a. 6.250
b. No correct answer
c. 10.825
d. 21.651
____
6. A triangle has an area of 7 in2, and two of the sides of the triangle have lengths 5 in. and 4 in. Find the angle
included by these two sides.
a. No correct answer
b. 0.795
c. 44.427
d. 45.573
____
7. Find the area of the shaded region in the figure if r = 6, and   129.
a.
b.
c.
d.
81.442
54.515
26.538
No correct answer
2
Name: ________________________
____
8. Solve for x correct to one decimal place.
a.
b.
c.
d.
e.
____
ID: A
519.6
477.8
692.8
173.2
367.6
9. A 78-ft tree casts a shadow that is 100 ft long. What is the angle of elevation of the sun?
a.
b.
c.
d.
e.
46.57
14.15
34.62
11.85
none of these
____ 10. Use the Law of Sines to find angle C. Let a = 28, and c = 13.
a.
b.
c.
d.
23
30
25
24
3
Name: ________________________
ID: A
____ 11. Use the Law of Cosines to determine side x if b = 9, c = 18, and   27.
a.
b.
c.
No correct answer
26.34
10.78
____ 12. Solve triangle ABC, if a = 17, b = 10, and C  117.
a.
b.
c.
d.
c = 23.31, A  40.53, B  22.47
c = 28.31, A  43.53, B  22.47
c = 23.31, A  35.02, B  27.98
c = 23.31, A  40.53, B  19.47
____ 13. Find the indicated angle  if a = 120, c = 135,   33. (Use either the Law of Sines or the Law of Cosines, as
appropriate.)
a.
b.
c.
81
85
95
____ 14. Find the equivalent expression.
tan 4 x  sec 4 x
a. cot 2 x  csc 2 x
b. csc 2 x  cot 2 x
c. csc 2 x  tan 2 x
d. tan 2 x  sec 2 x
e. sec 2 x  tan 2 x
4
Name: ________________________
ID: A
____ 15. Simplify the following trigonometric expression.
sec 2 x  1
sec 2 x
a. 1
b. sin x
c. sin 2 x
d. sec 2 x
____ 16. Simplify the following trigonometric expression.
sin(z) + cos(–z) + sin(–z)
a. sin z
b. cos z
c. 2sin z – cos z
d. 2sin z
____ 17. Simplify the following trigonometric expression as much as possible.
sin 2 t + cos 2 t + tan 2 t
a. tan x
b. sec 2 x
c. sec x
d. tan 2 x
____ 18. Simplify the following trigonometric expression as much as possible.
sin x
1  cos x

1  cos x
sin x
a. 2 sin x
b. cos x
c. sin x
d. 2 csc x
____ 19. Simplify the following trigonometric expression as much as possible.
sec 2 y  tan 2 y
a.
b.
c.
d.
csc 2 y
csc x
tan x
sin 2 x
sec 2 x
5
Name: ________________________
ID: A
____ 20. Find the equivalent expression.
1  sin x 1  sin x

1  sin x 1  sin x
a. 4tanx sec x
b. 4cot x sec x
c. 4 cot x csc x
d. 4cot x csc x
e. 4 tanx sec x
____ 21. Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume
0t

2
.
x 2  1 , x  sec t
a. 1
b. cos t
c. tan t
d. sec t
____ 22. Use an addition or subtraction formula to find the exact value of the expression.
tan (255)
a. 1  3
1
b. 2 
3
c.
d.
2
3
1
1 
3
____ 23. Use an addition or subtraction formula to find the exact value of the expression.
ÁÊ  ˜ˆ
cos ÁÁÁÁ ˜˜˜˜
Ë 12 ¯
 6
a.
4
2
b.
6
4
2
c.
6
4
2
d.
2
4
6
6
Name: ________________________
ID: A
____ 24. Simplify the following expression.
ÊÁ
 ˆ˜
sinÁÁÁ u  ˜˜˜˜
ÁË
2¯
a. sin u
b. –cos u
c. cos u
d. –sin u
____ 25. Simplify the following expression.
sin(v + x) – sin(v – x)
a. 2cos(v)cos(x)
b. 2sin(x)sin(v)
c. 2cos(v)sin(x)
d. 2cos(x)sin(v)
7
ID: A
Practice Test2
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
B
C
D
C
C
C
C
E
D
C
A
B
D
C
B
B
D
C
E
C
C
B
B
C
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1