Download ExamView - 2012-2113 Midterm Review.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
Trig/Pre-Calc B Midterm Review - 2012-13
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Graph the function. Which choice gives the amplitude, period, phase shift, and vertical shift for the function?
ÁÊÁ
1 ˜ˆ˜
y = 4sin ÁÁÁÁ 2θ + π ˜˜˜˜ − 3
ÁË
2 ˜¯
a.
c.
1
4; π ; – π ; –3
4
1
−4; π ; – π ; 3
4
b.
d.
1
4; π ; – π ; –3
4
1
−4; π ; – π ; –3
4
____
2. Which sum or difference identity would you use to verify that cos (180° − θ) = −cos θ?
a. cos (α −β ) = cos α cosβ + sin α sin β
b. sin (α + β ) = sin α cos β + cos α sin β
c. sin (α −β ) = sin α cos β – cos α sin β
d. cos (α −β ) = cos α cos β – sin α sin β
1
Name: ________________________
____
ID: A
3. Which double-angle or half-angle identity would you use to verify that
2tanx
a.
tan2x =
b.
sin2x = 2sinx cos x
2
1 − tan x
x
=±
c.
sin
d.
cot 2x =
2
sin2x
2sin 2 x
= cot x?
1 − cos x
1 + cos x
2sinx
1 − sin2 x
Short Answer
4. Find the exact value of cos 15°.
5. Change 2.99 radians to degree measure. Round to the nearest tenth.
ÊÁ 1
ˆ˜
Á
˜
6. Graph y = sec ÁÁÁÁ θ + 3π ˜˜˜˜ + 3 .
ÁË 2
˜¯
7. Use a graph of the sine function to find the value of θ for which sin θ = −1.
8. If sin θ =
3
5
and θ terminates in the first quadrant, find the exact value of cos 2θ.
9. Solve 5tanx = 5 3 for 0° ≤ x ≤ 180°.
10. Find the exact value of cos 105°.
11. A gear of radius 4.6 cm turns at 3 revolutions per second. What is the linear velocity of the gear in
centimeters per second?
12. What basic trigonometric identity would you use to verify that cot x sin x = cos x?
13. What basic trigonometric identity would you use to verify that tan x cos x = sin x?
14. Find sec x if tan2 x =
1
2
.
15. Solve 2 − 3cos x = 5 + 3cos x for 0° ≤ x ≤ 180°.
16. Find the area of a sector with a central angle of 111° and a radius of 19.3 millimeters. Round to the nearest
tenth.
17. What basic trigonometric identity would you use to verify that
18. Given sinθ =
19. Find cos x if
6
and secθ < 0, find cosθ and tanθ.
11
sin 2 x − 1
cos x
= −1.
20. Find cot x if sin x cot x csc x =
2.
2
sinx + 1
sinx
= 1 + csc x ?
Name: ________________________
ID: A
21. For a circle of radius 5 feet, find the arc length s subtended by a central angle of 65°.
22. If α and β are the measures of two first quadrant angles and sin α =
4
5
and sin β =
5
13
,
find sin (α + β ).
23. Find the amplitude, period, and phase shift of f (x ) = −4 sin (3x + 1).
24. Solve tanx = cot x for 0 ≤ x ≤ π.
25. Change 310° to radian measure in terms of π.
3
26. If sin θ = − and θ terminates in the fourth quadrant, find the exact value of tan 2θ.
5
27. Write an equation for the given function given the period, phase shift, and vertical shift.
2
2
cosecant function, period = π, phase shift = π, vertical shift = 3
7
9
28. What basic trigonometric identity would you use to verify that
sin2 x + cos 2 x
cos x
= sec x ?
29. Solve tanx sec x − 2tanx = 0 for all real values of x.
30. Write an equation of the cosine function with amplitude 3 and period 6π.
31. A truck driver travels at 60 miles per hour. The truck tires have a diameter of 26 inches. What is the angular
velocity of the wheels in revolutions per second (rps)?
32. Use a half-angle identity to find the exact value of tan 105°.
33. Write an equation of the sine function with the given amplitude, period, phase shift, and vertical shift.
2
2
amplitude: 4, period = π , phase shift = – π , vertical shift = 1
3
9
34. Find cos x if sin x cot x = 4.
35. Find csc x if sin x + cot x cos x =
36. Solve cos θ ≥
3
2
3.
for 0 ≤ θ ≤ 2π.
ÊÁ 1 ˆ˜ ˜ˆ˜
ÁÊÁ
37. Find the value of tanÁÁÁ sin -1 ÁÁÁÁ − ˜˜˜˜ ˜˜˜ .
Á
Ë 2 ¯ ˜¯
Ë

→
38. Identify the ordered pair that represents the vector from A ÊÁË −3, 1ˆ˜¯ to B ÊÁË 2, − 2 ˆ˜¯ and the magnitude of AB .
ä = 2, − 1, − 7 and ä
ä − 2v
ä.
39. Given u
v = −2, 3, − 3 find an ordered triple that represents 3u
3
Name: ________________________
ID: A
40. State the amplitude, period, phase shift, and vertical shift for the function. Then graph the function.
ÊÁ
3 ˆ˜˜
Á
y = −2 cos ÁÁÁÁ 3θ − π ˜˜˜˜ + 3
ÁË
2 ˜¯
ÊÁ 1
ˆ˜
ÁÁ
˜
Á
41. Graph y = tan ÁÁ θ − 3π ˜˜˜˜ + 3.
ÁË 2
˜¯
42. Verify that cos 2 x = sec 2 x − tan 2 x − sin2 x is an identity.
4