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# QUESTION 1 apoints m Given AABC with a = 19, mAA = 108' , and sz = 3 3' , find b. Round the sine value to the nearest thousandth and answer to the...

• Use the law of sines to solve triangles.
• Use law of cosines to solve triangles.
• Determine the number of solutions in an ambiguous case of law of sines.
• Use counterexamples and identities to disprove a mathematical statement.
• Verify and simplify equations and expressions using trigonometric identities.
• Evaluate expressions and find exact values using identities.
• Solve trigonometric equations.
• Find the area of a triangle using several different formulas, including Hero's formula.
• Find the arc length of an arc given the measure of the corresponding central angle and the radius of the circle.
• Find the area of a sector given the measure of the corresponding central angle and the radius of the circle.
• Determine angular displacement.
• Calculate linear velocity.
• Calculate angular velocity.
• Convert between units using dimensional analysis.

Now it's time to complete the unit exam.

QUESTION 1 apoints m Given AABC with a = 19, mAA = 108‘ , and sz = 3 3‘ , find b. Round the sine value to the nearest thousandth and answer to
the nearest hundredth. A 39.00
0 17.83
(3 15.39 0 10.88 QUESTION 2 (Spain‘s SaveAnswer Given AABC with a = 19, mAA = 10 1° , and {1143 = 3 6&quot; , find c. Round the sine value to the nearest thousandth and the
answer to the nearest hundredth. 0 43.00
A 19.45
0 16.67 O 13.20 QUESTION 3 3points _ SaveAnswer Given AABC with b = 19, c = 26, and m A = 1 24‘ , find a. Round the cosine value to the nearest thousandth and answer to the
nearest hundredth. 0 17.49
(3 25.51
(3 32.56 A 39.87

QUESTION 4 3points SaveAnswar Given AABC with a = 45, b = 10, and c = 45, find m 43 . Round the cosine value to the nearest thousandth and answer to the
nearest whole degree. (&gt;124°
(3 56°
C) 28° 0 13° QUESTION 5 3poinls m Given AABC with a = 9, b = 15, and mAA = 28‘ , find the number of distinct solutions. .0 no solutions
0 one solution
.0 two solutions 0 three solutions QUESTION 6 3 points SaveAnswer
Given AABC with a = 11.4, b = 12.8, and {1144 = 58‘ , find both possible values for ”143 . 9 70°
[3 72°
9 108° [3 no solution

QUESTION 7 3poinis SaveAnswer ‘ Given AABC with a = 4, b = 6.2, and &quot;14,4 = 25c , determine both possible values for MAB . r] 41°
r] 51°
r] 139° (3 no solution QUESTION 8 Spoints SaveAnswer Which of the following counterexamples proves that csc xtan x = cos x is not a trigonometric identity? Select all that apply. D D ‘3
El will kl: ‘3 D QUESTION 9 3p0int8 SaveAnswer Which of the following possible trigonometric identities can be verified? Select all that apply. 9 cosxtanx = S il'lX
D tanxsecxsinx =1 O tanxcscxsinx =1 9 cscxcotxsecx = csczx

QUESTION 10 apoinB SaveAnswer Which of the following possible trigonometric identiﬁes can be verified? Select all that apply. C] m =c5c2x_5ec2x sinxcosx
O cotx—tanx = 2 2
sinxcotx CSC x+sec X D slnx +cosxcotx =slnx D :2; =cosx ouesnon 11 3pm w Find the exact value for S &quot;(7—3 — L; . OO
1
05 O1
02 QUESTION 12 3points Find the exact value for tan 9?&quot; .
0 J5 — 1
O 1+ {5

QUESTION 13 4poinls SaveAnswer Find the exact value for 5 “1L; - %) . TTI’PlPar-sranhﬂlml diam-n) =155~i5~r~1~o I: 3%
XDDQﬁﬂEEEEEEfoya’a-qr——H-v
OIx-n-Wvluracaiﬂﬂﬂaaeeammmm- Path: p Words:0 A QUESTION 14 3points
Solve the following equation for 0 s x s 17 : 8COSZX _ ECOSX = 0 . Select all that apply.
[3 0
E
6
E
D 2
5 _T&quot;
6 QUESTION 15 [ 3p0ints SaveAnswer Solve the following equation for O 5 x 5 n’ : 5 inx + 4 = 5 . Select all that apply. [3
MI:

QUESTION 16 3points SaveAnswer Find the area of a triangle with side lengths of 2.5, 10.2. and 9 units. Round the answer to the nearest hundredth. O 14.20 units
0 10.40 units
O 15.92 units 0 11.83 units QUESTION 17 4points Find the area of a triangle with sides lengths 74.5, 50 and 50 units. Round the answer to the nearest hundredth. '1' T 1!!! [Paragraph :HArIaI :Hampt) ﬁg. ’3. T‘I'Q a 3%
xnnqnagéé *=='_—='r&quot;r,c9a'a-qr—-H-.
015. 9W'1“©©J—Eﬂﬁﬁﬁﬁﬁﬂiﬁiﬁﬁﬁﬂmwum Path: p Words:0 4 QUESTION 18 Spoints SaveAnswer Find the arc length of a circle if the central angle measures 90c and the radius measures 40 inches. Leave your answer in terms of Tr O 511' inches
0 1011’ inches
0 2 Orr inches 0 4011' inches

QUESTION 19 ' 4points SaveAnswer Find the arc length of a circle if the central angle measures 120° and the radius measures 6 inches. Leave your answer in terms of Tr . '1' T I 5!! [Paragraph :HArial :H'3(12pt) :l E . E v '1‘ . ’ v Q I: i x R as D an rm sass ’_—=‘:: T’T, (nan-q .. ——s[§'|. o It ﬁlhullups v 11' “ © © é @ In— I: F.‘ E'- I-tzu- :: :1: 1: HTML [55 Path:p Words:0 A
QUESTION 20 apoints SaveAnswer Find the area of a sector of a circle if the central angle measures 90c and the radius measures 20 inches. Leave your answer in terms
of IT . (710nm?
A 25rrin2
a”? 501'rin2 CiOOnmz QUESTION 21 apoinus SaveAnswer ' Find the area of a sector of a circle if the central angle measures 45&quot; and the radius measures 8 inches. Leave your answer in terms
of 11' . A 8min“
A 16nin‘
A 64nin“ CiOOan

QUESTION 22 4points SaveAnswar Find the angular displacement of 32.2 revolutions. Use Tl’ = 3, 14 . Round the answer to the nearest tenth. Show all work. '1' T I!!! [Paragraph #HArlal ¢H3(12pt) :1 55.37:”. T&quot; Q a!
xDDQﬂﬁ§§§§§§fT,éa 5'11-——._.-
0!: sw'1“©©&amp;ﬂﬂseaaﬁsmmmmm Path: p Words:0 A QUESTION 23 4points Determine the angular velocity in radians per second of 4.9 revolutions in 5 seconds. Use 1T = 3_ 14 . Round the answer to the
nearest tenth. Show all work. '1' TI!!! [Paragraph ¢HArlal :Hsuzpt) :':=.i:_ . T’I’Q a:
3600‘: ﬁﬁ§§§=’=='_—=T’T,o9a'=wr——H-v

QUESTION 24 3points Save Answer I Determine the linear velocity of an object with an angular velocity of 8.1 radians per second at a distance of 10 centimeters from the
center. Use 1T = 3, 14 . Round the answer to the nearest tenth. O 81.0 centimeters per second
F“ 47.0 centimeters per second
A 62.0 centimeters per second 0 98.0 centimeters per second QUESTION 25 3points Save Answer If a wheel with a radius of 70 inches spins at a rate of 600 revolutions per minute, find the approximate linear veiocity in miles per
hour. Use 11’ =3.14. C 105 miles per hour
0 250 miles per hour
O 214 miles per hour A 331 miles per hour

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