examview - precalc semester 2 final exam study guide€¦ · precalculus: semester 2 final exam...
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Name: ________________________ Class: ___________________ Date: __________ ID: A
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PreCalculus: Semester 2 Final Exam Study Guide
Short Answer
1. Draw the angle.
-
2. Convert the angle to a decimal in degrees.
Round the answer to two decimal places.
22°54'35''
3. Convert the angle to D° M' S'' form. Round the
answer to the nearest second.
183.82°
4. If s denotes the length of the arc of a circle of
radius r subtended by a central angle θ, find the
missing quantity. Round to one decimal place, if
necessary.
r = 14.8 inches, θ = 315°, s = ?
5. Convert the angle in degrees to radians. Express
the answer as multiple of ππππ.
54°
6. Convert the angle in radians to degrees.
7. If A denotes the area of the sector of a circle of
radius r formed by the central angle θ, find the
missing quantity. If necessary, round the answer
to two decimal places.
r = 7 feet, A = 56 square feet, θ = ?
8. In the problem, t is a real number and P = (x, y)
is the point on the unit circle that corresponds to
t. Find the exact value of the indicated
trigonometric function of t.
( , ) Find sec t.
9. Find the exact value. Do not use a calculator.
sin 2π
10. Find the exact value. Do not use a calculator.
csc (- )
11. Find the exact value of the expression. Do not
use a calculator.
tan - cos
12. A point on the terminal side of an angle θ is
given. Find the exact value of the indicated
trigonometric function of θ.
(3, -2) Find tan θ.
13. Use the fact that the trigonometric functions are
periodic to find the exact value of the
expression. Do not use a calculator.
csc 540°
14. Name the quadrant in which the angle θ lies.
csc θ > 0, sec θ > 0
Name: ________________________ ID: A
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15. In the problem, sin θ and cos θ are given. Find
the exact value of the indicated trigonometric
function.
sin θ = , cos θ = Find sec θ.
16. Find the exact value of the indicated
trigonometric function of θ.
tan θ = , 180°< θ < 270° Find cos θ.
17. Use the even-odd properties to find the exact
value of the expression. Do not use a calculator.
csc (-60°)
18. Use transformations to graph the function.
y = 5 sin x
19. Graph the function.
y = cot x + 1
20. Find the exact value of the expression.
sin-1
21. Find the exact value of the expression. Do not
use a calculator.
sin-1
22. Find the exact value of the expression.
sin
23. Find the exact value of the expression.
tan
24. Find the exact value of the expression.
sin 265° cos 25° - cos 265° sin 25°
Name: ________________________ ID: A
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25. Find the exact value under the given conditions.
26. Find the value of the indicated trigonometric
function of the angle θ in the figure. Give an
exact answer with a rational denominator.
Find sec θ.
27. Solve the right triangle using the information
given. Round answers to two decimal places, if
necessary.
a = 8, B = 30°; Find b, c, and A.
28. Solve the problem.
A radio transmission tower is 150 feet tall. How
long should a guy wire be if it is to be attached 5
feet from the top and is to make an angle of 20°
with the ground? Give your answer to the nearest
tenth of a foot.
29. Solve the triangle.
B = 20°, C = 30°, a = 2
30. Two sides and an angle are given. Determine
whether the given information results in one
triangle, two triangles, or no triangle at all.
Solve any triangle(s) that results.
a = 26, b = 20, B = 15°
31. Find the area of the triangle. If necessary, round
the answer to two decimal places.
A = 23°, b = 9,
32. Plot the point given in polar coordinates.
33. The polar coordinates of a point are given. Find
the rectangular coordinates of the point.
(4, 70°) Round the rectangular coordinates to two
decimal places.
34. The letters x and y represent rectangular
coordinates. Write the equation using polar
coordinates (r, θ).
5x + 7y = 9
Name: ________________________ ID: A
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35. Transform the polar equation to an equation in
rectangular coordinates. Then identify and
graph the equation.
r = 2 sin θ
36. Plot the complex number in the complex plane.
-8 + i
37. Find zw or as specified. Leave your answer
in polar form.
z = 10(cos 45° + i sin 45°)
w = 5(cos 15° + i sin 15°)
Find .
38. Write the expression in the standard form a +
bi.
3
39. Find all the complex roots. Leave your answers
in polar form with the argument in degrees.
The complex fifth roots of -2i
40. Use the vectors in the figure below to graph the
following vector.
2u - z - w
41. Find the indicated quantity.
Find u + v given u = -9i - 4j and v = -7i + 9j.
42. Find the quantity if v = 5i - 7j and w = 3i + 2j.
+
43. Use the TABLE feature of a graphing utility to
find the limit.
Name: ________________________ ID: A
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44. Use the graph shown to determine if the limit
exists. If it does, find its value.
f(x)
45. Use the grid to graph the function. Find the
limit, if it exists
f(x), f(x) =
46. Find the limit algebraically.
lim (x - )(x + )
47. Find the one-sided limit.
(x2 - 3x - 5)
48. Determine whether f is continuous at c.
f(x) = ; c = 7
49. Determine whether f is continuous at c.
f(x) = ; c = 1
50. Find the numbers at which f is continuous. At
which numbers is f discontinuous?
f(x) =
51. Find the slope of the tangent line to the graph at
the given point.
f(x) = x2 + 5x at (4, 20)
52. Find the derivative of the function at the given
value of x.
f(x) = x3 + 4x; x = -2
Essay
53. Prove:
ID: A
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PreCalculus: Semester 2 Final Exam Study Guide
Answer Section
SHORT ANSWER
1. ANS:
PTS: 1
2. ANS:
22.91°
PTS: 1
3. ANS:
183°49'12''
PTS: 1
4. ANS:
81.4 in.
PTS: 1
5. ANS:
PTS: 1
6. ANS:
36°
PTS: 1
7. ANS:
2.29 radians
PTS: 1
8. ANS:
PTS: 1
ID: A
2
9. ANS:
0
PTS: 1
10. ANS:
0
PTS: 1
11. ANS:
-
PTS: 1
12. ANS:
-
PTS: 1
13. ANS:
undefined
PTS: 1
14. ANS:
I
PTS: 1
15. ANS:
PTS: 1
16. ANS:
-
PTS: 1
17. ANS:
2
PTS: 1
ID: A
3
18. ANS:
PTS: 1
19. ANS:
PTS: 1
20. ANS:
PTS: 1
21. ANS:
PTS: 1
ID: A
4
22. ANS:
PTS: 1
23. ANS:
2 -
PTS: 1
24. ANS:
-
PTS: 1
25. ANS:
PTS: 1
26. ANS:
sec θ =
PTS: 1
27. ANS:
b = 4.62
c = 9.24
A = 60°
PTS: 1
28. ANS:
424.0 ft
PTS: 1
29. ANS:
A = 130°, b = 0.89, c = 1.31
PTS: 1
30. ANS:
two triangles
A1 = 19.66°, C1 = 145.34°, c1 = 43.95 or
A2 = 160.34°, C2 = 4.66°, c2 = 6.28
PTS: 1
ID: A
5
31. ANS:
3.52
PTS: 1
32. ANS:
PTS: 1
33. ANS:
(1.37, 3.76)
PTS: 1
34. ANS:
r(5 cos θ + 7 sin θ) = 9
PTS: 1
35. ANS:
x2 + (y - 1)2 = 1; circle, radius 1, center at (0, 1) in rectangular coordinates
PTS: 1
ID: A
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36. ANS:
PTS: 1
37. ANS:
2(cos 30° + i sin 30°)
PTS: 1
38. ANS:
-4 - 4 i
PTS: 1
39. ANS:
(cos 54° + i sin 54°), (cos 126° + i sin 126°), (cos 198° + i sin 198°), (cos 270° + i sin 270°),
PTS: 1
40. ANS:
PTS: 1
41. ANS:
-16i + 5j
PTS: 1
ID: A
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42. ANS:
+
PTS: 1
43. ANS:
2
PTS: 1
44. ANS:
2
PTS: 1
45. ANS:
-1
PTS: 1
46. ANS:
-5
PTS: 1
47. ANS:
-1
PTS: 1
48. ANS:
not continuous
PTS: 1
49. ANS:
not continuous
PTS: 1
50. ANS:
continuous for all real numbers except x = -2 and x = 2
PTS: 1
51. ANS:
13
PTS: 1
52. ANS:
16
PTS: 1
ID: A
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ESSAY
53. ANS:
PTS: 1