Download Review for precal final

Final Exam Review
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) Find the complement of an angle whose measure is 36°22 .
A) 54°37
B) 53°38
C) 53°22
2) Find the supplement of an angle whose measure is 37°39 1
A) 142°21 59
B) 52°20 59
C) 142°20 59
Perform the calculation.
3) 23°44 + 47°32
A) 17°16
4) 90° - 30°10 48
A) 59°50 12
D) 54°38
D) 52°21 59
B) 17°76
C) 71°76
D) 71°16
B) 59°49 11
C) 59°49 12
D) 60°50 12
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
5) 53°39 2
A) 53.66°
B) 53.61°
C) 53.71°
D) 53.65°
Convert the angle to degrees, minutes, and seconds.
6) 45.28°
A) 45°16 48
B) 45°16 28
D) 45°16 54
C) 45°16 36
Find the angle of smallest possible positive measure coterminal with the given angle.
7) 449°
A) 269°
B) 224.5°
C) 89°
8) -54°
A) 486°
B) 54°
C) 126°
D) 79°
D) 306°
1)
2)
3)
4)
5)
6)
7)
8)
Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
9) (3, 4); Find sin .
9)
3
3
4
4
A)
B)
C)
D)
5
4
3
5
10) (9, 12); Find cos .
3
A)
5
4
B)
5
4
C)
3
1
3
D)
4
10)
Evaluate the function requested. Write your answer as a fraction in lowest terms.
11)
11)
15
9
12
Find sin A.
A) sin A =
5
4
B) sin A =
3
5
C) sin A =
4
3
D) sin A =
Without using a calculator, give the exact trigonometric function value with rational denominator.
12) tan 45°
2 3
1
A)
B) 2
C) 1
D)
2
3
4
5
12)
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using
the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize
the denominator if applicable.
13) Find tan B when a = 48 and c = 50.
13)
7
24
7
24
A)
B)
C)
D)
25
25
24
7
Solve the problem.
14) Find the exact value of x in the figure.
14)
x
20
A)
34 3
3
Give the exact value.
15) cos 210°
3
A)
2
40 6
3
C) 39 6
2
B) 2
3
C) 2
B)
D)
10 6
3
D)
2
2
15)
2
Find a value of in [0°, 90°) that satisfies the statement. Leave answer in decimal degrees.
16) cos = 0.11988773
A) 83.1143768°
B) 6.88562321°
C) 96.8856232°
D) 276.885623°
Solve the right triangle.
17) a = 1.9 cm, b = 1.7 cm, C = 90°
A) A = 48.2°, B = 41.8°, c = 2.5 cm
C) A = 63.5°, B = 26.5°, c = 3.6 cm
B) A = 43.7°, B = 46.3°, c = 2.5 cm
D) A = 41.8°, B = 48.2°, c = 2.5 cm
Solve the problem.
18) From a boat on the lake, the angle of elevation to the top of a cliff is 23°4'. If the base of the cliff is
919 feet from the boat, how high is the cliff (to the nearest foot)?
A) 394 ft
B) 404 ft
C) 391 ft
D) 401 ft
Convert the angle to radians. Leave as a multiple of .
19) 30°
A)
8
B)
C)
7
5
D)
20)
C) 360.00°
B) 1
1
C)
2
D) 0
C) 0.2261
D) 0.9741
Use a table or a calculator to evaluate the function.
22) tan 0.2281
A) 0.2321
B) 1.027
D) 359.50°
21)
Give the amplitude or period as requested.
23) Amplitude of y = 3 sin x
A)
3
24) Period of y = sin 5x
A) 5
Find the specified quantity.
25) Find the period of y = -3 sin
A) 3
18)
6
B) 361.00°
Find the exact circular function value.
21) cos 2
A) -1
17)
19)
Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
10
20)
5
A) 360.50°
16)
22)
23)
B) 3
C) 2
D) 3
24)
2
B)
5
C) 2
D) 1
1
x.
2
2
25)
B) 4
C)
3
2
D) 2
Use the fundamental identities to find the value of the trigonometric function.
2
26) Find sin if cos = and is in quadrant IV.
3
A)
5
4
B)
27) Find tan s if sin s =
7
9
A) -
3 7
7
5
3
C) -
26)
D) -
3
2
3
and s is in quadrant II.
4
B)
27)
5
4
C) -
3 7
7
D) -
3
2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Verify that each equation is an identity.
28) (sec - tan )(sec + tan ) = 1
29)
28)
1 + cos t 1 - cos t
= 4 cot t csc t
1 - cos t 1 + cos t
29)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use an appropriate identity to find the exact value of the expression.
11
30) sin
12
2( 3 - 1)
4
A)
31) cos
B)
-
2( 3 - 1)
4
30)
2( 3 + 1)
4
C)
D)
-
2( 3 + 1)
4
31)
12
A)
-
2( 3 + 1)
4
2(1 4
B)
3)
2(1 +
4
C)
3)
2( 3 - 1)
4
D)
32) tan (165°)
A) 2 -
32)
3
33) sin (165°)
2( 3 - 1)
A)
4
2- 3
B)
4
-2 + 3
C)
4
D) -2 +
3
33)
B)
-
2( 3 + 1)
4
C)
Find the exact value by using a sum or difference identity.
34) sin (15°) cos (45°) + cos (15°) sin (45°)
3
3
A)
B)
3
2
-
2( 3 - 1)
4
2( 3 + 1)
4
D)
34)
C)
4
1
2
D)
1
4
35) sin (125°) cos (65°) - cos (125°) sin (65°)
3
3
A)
B)
2
3
35)
C)
Solve the triangle.
36) B = 30.8°
C = 114.4°
b = 39.86
A) A = 34.8°, a = 46.43, c = 72.89
C) A = 32.8°, a = 70.89, c = 44.43
1
2
D)
25
12
36)
B) A = 32.8°, a = 72.89, c = 46.43
D) A = 34.8°, a = 44.43, c = 70.89
Find the missing parts of the triangle.
37) A = 30.0°
a = 17.57
b = 35.14
A) no such triangle
C) B = 60.0°, C = 60.0°, c = 30.43
37)
B) B = 90.0°, C = 60.0°, c = 30.43
D) B = 60.0°, C = 90.0°, c = 30.43
38) B = 46°20'
b = 13.84
a = 21.22
A) no such triangle
C) A = 44°10', C = 89°30', c = 35.06
38)
B) A = 45°10', C = 90°30', c = 36.56
D) A = 42°10', C = 91°30', c = 32.06
39) B = 21.5°
b = 2.72
a = 3.71
A) A = 29.99°, C = 128.51°, c = 5.81
39)
B) no such triangle
C) A = 150.01°, C = 8.49°, c = 1.1
D) A1 = 29.99°, C1 = 128.51°, c1 = 5.81;
A2 = 150.01°, C2 = 8.49°, c2 = 1.1
40) C = 108.5°
a = 5.60 km
b = 10.80 km
A) c = 19.5 km, A = 20.8°, B = 50.7°
C) c = 13.7 km, A = 22.8°, B = 48.7°
40)
B) No triangle satisfies the given conditions.
D) c = 16.6 km, A = 24.8°, B = 46.7°
Find the missing parts of the triangle. (Find angles to the nearest hundredth of a degree.)
41) a = 8.7 in.
b = 13.0 in.
c = 15.6 in.
A) A = 35.90°, B = 54.45°, C = 89.65°
B) A = 33.90°, B = 56.45°, C = 89.65°
C) No triangle satisfies the given conditions.
D) A = 31.9°, B = 56.45°, C = 91.65°
5
41)
Find the area of triangle ABC with the given parts.
42) a = 8.1 cm
b = 14.6 cm
c = 15.2 cm
A) 61 cm2
B) 58 cm2
C) 64 cm2
D) 67 cm2
Find the indicated vector.
43) Let a = 3i, b = i + j. Find 3a + b.
A) 10i + 3j
B) 10i + j
C) i + 10j
D) 11i + j
C) 6, 18
D) -6, -18
44) Let a = -1, -3 . Find 6a.
A) 6, -18
42)
B) -6, 18
45) Let a = -8, -6 , b = -3, 9 . Find b - a.
A) 17, 3
B) -11, 3
C) 2, 12
D) 5, 15
43)
44)
45)
Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
46) 7, 7
46)
A) 14; 45°
B) 7; 225°
C) 7 2; 45°
D) 7 2; 225°
Give the focus, directrix, and axis for the parabola.
47) x2 = 16y
A) (0, -4), x = -4, x-axis
C) (0, 4), y = -4, y-axis
B) (4, 0), x = 4, x-axis
D) (4, 0), y = 4, y-axis
48) (y - 5)2 = -4(x + 4)
A) (-5, 5), x = -3, y = 5
C) (-5, 5), x = -3, y = -4
B) (-5, 4), x = -3, y = 5
D) (-5, 5), x = -4, y = 5
Match the equation of the parabola with the appropriate description.
49) y - 14 = 2(x + 3)2
A) Vertex at (3, -14)
B) Vertex at (-3, 14)
C) Vertex at (-14, 3)
D) Vertex at (14, -3)
50) y - 3 = 2(x - 5)2
A) Vertex at (-10, -3)
C) Vertex at (10, 3)
B) Vertex at (5, 3)
D) Vertex at (-5, -3)
6
47)
48)
49)
50)
Answer Key
Testname: REVIEW FOR PRECAL FINAL
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)
26)
27)
B
C
D
C
D
A
C
D
D
A
D
C
C
B
C
A
A
C
D
C
B
A
D
B
B
C
C
28) (sec - tan )(sec + tan ) = sec2 - tan2 = 1
1 + cos t 1 - cos t
(1 + cos t)2 - (1 - cos t)2
1 + 2 cos t + cos2t - (1 - 2 cos t + cos2 t)
4 cos t
4 cos t
1
=
=
=
=
·
29)
1 - cos t 1 + cos t
sin t
sin t
1 - cos2 t
1 - cos2 t
sin 2 t
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
= 4 cot t csc t
A
C
D
A
B
A
D
B
A
D
C
B
B
B
D
D
C
C
7
Answer Key
Testname: REVIEW FOR PRECAL FINAL
48) A
49) B
50) B
8