Trigonometry - Additional Questions: Sheet 1
1.) x = 30° Find sin(x) , cos(x), and tan(x)
(TE1)
2.) x = 60° Find sin(x), cos(x), and tan(x)
(TE1)
3.) Find cos-1(sin(60°))
(TE1)
4.) Find angle x if cos(x) = 0.5
(TE1)
5 ) x = 45° Find sin(x)
5.)
sin(x), cos(x),
cos(x) and tan(x)
(TE1)
6.) x = 15° Find sin(x), cos(x), and tan(x)
(TE1)
7.) Find sin-1(cos(30°))
(TE1)
8.) Find angle x if sin(x) = 0.315
(TE1)
9.) x = 90° Find sin(x), cos(x), and tan(x)
(TE1)
10.) x = 150° Find sin(x), cos(x), and tan(x)
(TE1)
Trigonometry - Additional Questions: Sheet 1 Answers
1.) x = 30° Find sin(x) , cos(x), and tan(x)
(TE1)
sin(30) = 0.5, cos(30) = 0.866, tan(30) = 0.577
2.) x = 60° Find sin(x), cos(x), and tan(x)
(TE1)
sin(60) = 0.866, cos(60) = 0.5, tan(60) = 1.732
3 ) Find cos-1(sin(60°)) = 30°
3.)
4.) Find angle x if cos(x) = 0.5
(TE1)
x = 60°
5.) x = 45° Find sin(x), cos(x), and tan(x)
(TE1)
(TE1)
sin(45) = 0.707, cos(45) = 0.707, tan(45) = 1
6.) x = 15° Find sin(x), cos(x), and tan(x)
(TE1)
sin(15) = 0.259, cos(15) = 0.966, tan(15) = 0.268
7.)) Find
Fi d sin
i -11(cos(30°))
(
(30°)) = 60°
8.) Find angle x if sin(x) = 0.315
(TE1)
x = 18.4
9.) x = 90°
90 Find sin(x), cos(x), and tan(x)
(TE1)
(TE1)
sin(90) = 1
1, cos(90) = 0,
0 tan(90) = undefined
10.) x = 150° Find sin(x), cos(x), and tan(x)
(TE1)
sin(150) = 0.5, cos(150) = -0.866, tan(150) = -0.577
Trigonometry - Additional Questions: Sheet 2
1.) Find sin(cos-1(0.5))
(TE1)
2.)) Find angle x if tan(x) = 0.425
2
0 425
(TE1)
3.) x = 117° Find sin(x), cos(x), and tan(x)
(TE1)
4.) x = 34.5° Find sin(x), cos(x), and tan(x)
(TE1)
5.) Find sin-1(tan(17°))
(TE1)
6.) Find angle x if sin(x) = - 0.5
(TE1)
7.) x = 100° Find sin(x), cos(x), and tan(x)
(TE1)
8 ) x = 0° Find
8.)
Fi d sin(x),
i ( ) cos(x),
( ) and
d tan(x)
t ( )
(TE1)
9.) Find tan-1(cos(70°))
(TE1)
10.) Find angle x if tan(x) = - 0.245
(TE1)
Trigonometry - Additional Questions: Sheet 2 Answers
-1((0.5))
1.)) Find sin(cos
(
)) = 0.866
(TE1)
(
)
2.) Find angle x if tan(x) = 0.425
x = 23.03° (TE1)
3.) x = 117° Find sin(x), cos(x), and tan(x)
(TE1)
sin(117) = 0.891, cos(117) = -0.454, tan(117) = -1.96
4.) x = 34.5° Find sin(x), cos(x), and tan(x)
(TE1)
sin(34.5) = 0.566, cos(34.5) = 0.824, tan(34.5) = 0.687
5.) Find sin-1(tan(17°)) = 17.8°
(TE1)
6.)) Find
6
Fi d angle
l x if sin(x)
i ( ) = - 0.5
05
(TE1)
x = 210°, 330° or -30°
7.) x = 100° Find sin(x), cos(x), and tan(x)
(TE1)
sin(100) = 0.985, cos(100) = -0.174, tan(100) = -5.67
8.) x = 0° Find sin(x), cos(x), and tan(x)
(TE1)
sin(0) = 0, cos(0) = 1, tan(0) = 0
9.) Find tan-1(cos(70°)) = 18.88°
(TE1)
10.) Find angle x if tan(x) = - 0.245
(TE1)
x = 166.2°, 346.2°, or -13.8°
Trigonometry - Additional Questions: Sheet 3
Sine of X - Find X in the following problems (TE2)
X
5
X
17
30°
60°
X°
X°
1250
3.5
8.4
785
X
120°
20
Trigonometry - Additional Questions: Sheet 3 Answers
Sine of X - Find X in the following problems (TE2)
X
5
X
17
x = 2.5
30°
60°
X°
x = 19.6
X°
x = 24.6°
1250
3.5
8.4
785
X
x = 40
120°
20
x = 38.9°
Trigonometry - Additional Questions: Sheet 4
Cosine of X - Find X in the following problems (T3E)
27.4°
x
x
12.5
33°
17
9
400
1000
x°
x°
5
18.5
x
145°
Trigonometry - Additional Questions: Sheet 4 Answers
Cosine of X - Find X in the following problems (T3E)
27.4°
x
x = 20.3
x
12.5
x = 14.1
33°
17
x = 66.4°
9
400
1000
x°
x°
5
x = 32.3
18.5
x
145°
x = 58.3°
Trigonometry - Additional Questions: Sheet 5
Tangent of X - Find X in the following problems (T4E)
x
70°
55°
12.5
17
2500
7.5
x°
4
2100
x°
138°
x
236
x
Trigonometry - Additional Questions: Sheet 5 Answers
Tangent of X - Find X in the following problems (T4E)
x = 4.55
x = 24.3
x
70°
55°
12.5
17
x = 28.1
28.1°
2500
7.5
x°
4
2100
x°
x = 49.9°
138°
x = 262.1
x
236
x
Trigonometry - Additional Questions: Sheet 6
Sin, Cosine, and Tangent - Angles and Signs (T5E)
y-axis
x°
180°
x-axis
270°
In the diagram above, the highlighted line rotates around in a circle
in the xy-plane, starting at 0° and ending at 360°. Fill in the + or -
0-90°
sin(x)
cos(x)
tan(x)
90-180°
180-270° 270-360°
Trigonometry - Additional Questions: Sheet 6 Answers
Sin, Cosine, and Tangent - Angles and Signs (T5E)
y-axis
x°
180°
x-axis
270°
In the diagram above, the highlighted line rotates around in a circle
in the xy-plane, starting at 0° and ending at 360°. Fill in the + or -
0-90°
90-180°
180-270° 270-360°
sin(x)
positive positive negative negative
cos(x)
tan(x)
positive negative negative positive
positive negative positive negative
Trigonometry - Additional Questions: Sheet 7
Law of Sines - Find X and Y in the following problems (T6E)
8
y
50°
40°
6.5
x°
70°
y
2552
50
98°°
y°
32
y
x°
x
87.5
25°
45
1115
1000
y°
80°
x
x
Trigonometry - Additional Questions: Sheet 7 Answers
Law of Sines - Find X and Y in the following problems (T6E)
8
40°
6.5
x°
y
x = 52.3°
y = 6.18
50°
x
70°
y
2552
x = 3130.5
y = 2885.1
50
98°°
y°
y
x°
87.5
x
32
x = 34.5°
y = 72.4
25°
45
x = 66.5
y = 36.5°
1115
1000
x = 697.1
y = 62°
y°
80°
x
Trigonometry - Additional Questions: Sheet 8
Law of Cosines - Find X and Y in the following problems
(T7E)
8
15.2
y°
40°
120°
13.5
y
5
x
48
y
x
1645
58°
80°
x°
2005
50
x
y°
4
5.5
50°
Trigonometry - Additional Questions: Sheet 8 Answers
Law of Cosines - Find X and Y in the following problems
(T7E)
8
15.2
y°
40°
120°
13.5
y
5
y = 5.26
x
x = 24.87
y = 28°
48
y
x
1645
58°
80°
x°
2005
50
x = 58.9°
y = 47.5
x
y°
5.5
x = 4.24
y = 83.6°
4
50°
x = 2362.3
Trigonometry - Additional Questions: Sheet 9 Answers
Areas of Irregular Triangles
(T7E)
39 mi
25 mi
8 in
5 in
6 in
43 mi
120 km
15.5 m
7.4 m
93m
9.3
65 km
115 km
Trigonometry - Additional Questions: Sheet 9 Answers
Areas of Irregular Triangles
(T7E)
39 mi
25 mi
8 in
5 in
6 in
43 mi
A = 14.98 in2
A = 482.1 mi2
120 km
15.5 m
7.4 m
65 km
115 km
93m
9.3
A = 23.9 m2
A = 3,659 km2