MCR3U
4.0a
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Find the measure of the indicated angle to the nearest degree.
1)
2)
?
?
56
40
52
38
3)
4)
?
41
5)
34
37
35
?
6)
33
22
?
?
8
34
Find the missing side. Round to the nearest tenth.
7)
8)
33
66° 32
52°
x
x
9)
10)
39
18°
x
39
65°
11)
x
12)
24
x
30°
31°
x
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38
Worksheet by Kuta Software LLC
Answers to 4.0a
1) 43°
5) 14°
9) 83.6
2) 50°
6) 69°
10) 12.7
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3) 59°
7) 53.6
11) 12.0
4) 23°
8) 71.9
12) 73.8
Worksheet by Kuta Software LLC
Extra Practice
Sine Law and Cosine Law
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Find each measurement indicated. Round your answers to the nearest tenth.
1) Find AC
2) Find BC
A
B
C
15°
92°
28°
C
10 yd
59°
A
B
15 yd
4) Find m∠A
3) Find AC
C
C
28 yd
7 yd
75°
A
B
83°
38°
B
25 m
A
5) Find m∠B
6) Find m∠C
C
A
98°
28°
11 ft
21 mi
B
A
32 mi
C
B
19 ft
Solve each triangle. Round your answers to the nearest tenth.
7)
8)
B
A
34°
22 cm
37°
24 km
109°
104°
C
A
C
B
9)
A
127°
C
34 m
20 m
B
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Worksheet by Kuta Software LLC
Find each measurement indicated. Round your answers to the nearest tenth.
11) Find AB
10) Find AB
A
A
B
13 in
93°
20 in
27 m
C
80°
C
B
19 m
13) Find m∠C
12) Find AC
A
14.5 in
B
97.5°
C
13.7 in
14 in
B
117°
8 in
C
A
14) Find m∠C
15) Find m∠A
A
B
14 in
B
6 in
9 in
16 mi
117°
C
C
A
28 mi
Solve each triangle. Round your answers to the nearest tenth.
16)
17)
B
C
25.6 mi
17.7 mi
33°
27 yd
21 yd
A
C
28.7 mi
B
A
18)
B
13 in
A
106°
27 in
C
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Worksheet by Kuta Software LLC
Answers to Sine Law and Cosine Law
1) 7 yd
2) 33.1 yd
5) 17.9°
6) 35°
8) m∠B = 39°, c = 37 km, a = 23 km
10) 30.2 m
11) 24.4 in
14) 137°
15) 22°
17) m∠A = 50.5°, m∠B = 96.5°, c = 14.8 yd
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3) 28.9 m
4) 14°
7) m∠C = 37°, b = 13 cm, c = 14 cm
9) m∠B = 25°, m∠C = 28°, b = 18 m
12) 19 in
13) 39.8°
16) m∠A = 61.7°, m∠B = 80.8°, m∠C = 37.5°
18) m∠A = 22.1°, m∠B = 51.9°, c = 33 in
Worksheet by Kuta Software LLC
MCR3U
4.2 Co-terminal Angles
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Find a positive and a negative coterminal angle for each given angle.
1) 690°
2) −10°
3) 270°
4) −15°
5) 55°
6) −55°
7) 95°
8) −285°
9) 105°
10) 60°
Find a coterminal angle between 0° and 360°.
11) 675°
12) 555°
13) 1020°
14) 780°
State if the given angles are coterminal.
15) 295°, −65°
16) 315°, −675°
17) 330°, −30°
18) 345°, 705°
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Worksheet by Kuta Software LLC
Answers to 4.2 Co-terminal Angles
1) 330° and −30°
5) 415° and −305°
9) 465° and −255°
13) 300°
17) Yes
2) 350° and −370°
6) 305° and −415°
10) 420° and −300°
14) 60°
18) Yes
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3) 630° and −90°
7) 455° and −265°
11) 315°
15) Yes
4) 345° and −375°
8) 75° and −645°
12) 195°
16) No
Worksheet by Kuta Software LLC
MCR3U
4.2b
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Solve each equation for 0 ≤ θ < 360.
360 Round your answers to the nearest hundredth.
1) sin θ = −1.19
3) cos θ = −1
5) −
3
= cos θ
2
2) sin θ = −0.32
4) −
2
= cos θ
2
6) cos θ = 0.59
7) sin θ = 0.17
8) −2.25 = tan θ
9) 1 = sin θ
10) 1 = tan θ
11) sin θ = −0.1
13) 3 + tan θ = −5.97
15)
1
cos θ = 0.0075
4
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12)
2 3
= sin θ
3
14) −0.2 = −1 + cos θ
16) −sin θ = −0.45
Worksheet by Kuta Software LLC
Answers to 4.2b
1) No solution.
5) {150, 210}
9) {90}
13) {96.36, 276.36}
2) {198.66, 341.34}
6) {53.84, 306.16}
10) {45, 225}
14) {36.87, 323.13}
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3) {180}
7) {9.79, 170.21}
11) {185.74, 354.26}
15) {88.28, 271.72}
4) {135, 225}
8) {113.96, 293.96}
12) No solution.
16) {26.74, 153.26}
Worksheet by Kuta Software LLC
MCR3U
4.3 Secondary Trig Ratios
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Find the value of the trig function indicated.
1) sec θ
2) cot θ
θ
4
15
5 10
5
θ
3) cot θ
4) cot θ
θ
15
θ
25
9
3 13
5) csc θ
6) csc θ
θ
8 5
θ
16
3
5
Find the value of each. Round your answers to the nearest ten-thousandth.
7) cot 47°
8) cot 75°
9) csc 50°
10) cot 60°
11) csc 15°
12) sec 40°
13) cot 5°
14) csc 60°
Use a calculator to find each. Round your answers to the nearest ten-thousandth.
15) tan 340°
16) cot 42°
17) csc 10°
18) sin 97°
19) sin 140°
20) sec 227°
21) cos 271°
22) sec 130°
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Worksheet by Kuta Software LLC
Answers to 4.3 Secondary Trig Ratios
1)
10
3 5
5
9) 1.3054
13) 11.4301
17) 5.7588
21) 0.0175
5)
4
3
3 5
6)
5
10) 0.5774
14) 1.1547
18) 0.9925
22) -1.5557
2)
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3
4
7) 0.9325
2
3
8) 0.2679
3)
4)
11) 3.8637
15) -0.3640
19) 0.6428
12) 1.3054
16) 1.1106
20) -1.4663
Worksheet by Kuta Software LLC
MCR3U
4.3
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Solve each equation for 0 ≤ θ < 360.
360
1) sin θ = −1
2) sec θ = −1
3) cos θ = 0
4) tan θ = 0
5) 0 = cot θ
6)
7) − 2 = sec θ
9) csc θ = −
2 3
3
11) sin θ = − 2
13) − 2 = csc θ
15) cot θ = −1
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3
= tan θ
3
8) cot θ = −
3
3
10)
2
= sin θ
2
12)
2 = sec θ
14) cos θ = −
2
2
16) 2 = csc θ
Worksheet by Kuta Software LLC
Answers to 4.3
1) {270}
5) {90, 270}
9) {240, 300}
13) {225, 315}
2) {180}
6) {30, 210}
10) {45, 135}
14) {135, 225}
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3) {90, 270}
7) {135, 225}
11) No solution.
15) {135, 315}
4) {0, 180}
8) {120, 300}
12) {45, 315}
16) {30, 150}
Worksheet by Kuta Software LLC
Unit 4 Review
31. a) {0,180,360} b) {0,360}
32. a) 5/2
b) -5/12
MCR3U
31. Solve the following a)
b) cos2x – 3cosx + 2 = 0
32. Give the exact value for the following (show all steps): a) sin45ocos135o-tan60otan300o
b) (sin210otan150o)2 +cos240o
33. Textbook – P. 277#12 p.279 #10