Download MATH 2412 Test 2 Review Spring 2017

Review - Test 2
MATH 2412 - Spring, 2017
Morales, Instructor
Use the information given about the angle , 0
2 , to
find the exact value of the indicated trigonometric
function.
3
Find cos (2 ).
12) sin = , 0 < <
5
2
Simplify the trigonometric expression by following the
indicated direction.
6 cos2 + 7 cos + 1
1) Factor and simplify:
cos2 - 1
Complete the identity.
sin
sin
2)
1 + sin
1 - sin
3)
sec sin
tan
4) cos
=?
-1=?
- cos
sin2
=?
Find the exact value of the trigonometric function.
5) sin 15° (Hint: Use 15 = 45 - 30)
2
<
<
<
3
; cos
2
15) sin
=-
3 3
,
<
5
2
=-
<
<
3
2
Find cos
<2
Find sin
2
2
Solve the equation on the interval 0
3
20) sin (4 ) =
2
Find cos ( + ).
<
3
,
5
19) cos (2 ) =
Find the exact value under the given conditions.
21
3
, 0 < < ; cos = , 0 < <
10) sin =
29
2
5
2
3
,
4
=-
Find sin (2 ).
.
2
2
.
Solve the equation. Give a general formula for all the
solutions.
3
18) sin =
2
9) cos 20° cos 40° - sin 20° sin 40°
=
14) cos
<2
17) cos 22.5°
5
(Hint:
= 75, and 75 = 30 + 45)
12
Find the exact value of the expression.
8) sin 25° cos 35° + cos 25° sin 35°
11) tan
=
Use the Half-angle Formulas to find the exact value of the
trigonometric function.
16) sin 22.5°
6) sin 165° (Hint: Use 165 = 45 + 120)
5
7) cos
12
24 3
,
<
25
2
13) cos
24
,
25
21) cos
Find sin ( + ).
-1=0
22) 2 cos
+1=0
23) cos2
+ 2 cos
24) sin2
+ sin
25) sin (2 ) + sin
1
+1=0
=0
=0
<2 .
Solve the equation for solutions in the interval [0°, 360°).
26) sin 2 = cos
27) sin 2 = -
Find the missing parts of the triangle.
35) B = 108.2°
a = 298 cm
b = 1351 cm
1
2
36) A = 124°
a = 1204 cm
b = 1304 cm
Let triangle ABC have standard labeling. Given the
following combination of angles and sides, decide
whether solving the triangle results in the ambiguous case.
28) A, c, and a
37) B = 23.0°
b = 16.41
a = 21
29) a, b, and c
38) C = 124.7°
a = 5.90 km
b = 10.61 km
30) b, B, and c
Assume triangle ABC has standard labeling. Determine if
AAS, ASA, SSA, SAS, or SSS is given and decide if the
law of sines or the law of cosines should be used to solve
the triangle.
31) a, b, and A
39) a = 7.0 in.
b = 13.6 in.
c = 16.4 in.
Provide an appropriate response.
40) Explain, in your own words, the situation
called "the ambiguous case of the law of sines."
32) A, b, and c
Solve the triangle.
33)
41) Explain why the law of sines cannot be used to
solve a triangle if we are given the lengths of
two sides and the measure of the included
angle.
23 m
Find the area of the triangle using one of the area
formulas.
42) a = 19.7 cm
b = 15.9 cm
c = 16.6 cm
34)
43) b = 7.9 in.
A = 29.33°
C = 71.33°
9
Solve.
2
44) Two tracking stations are on the equator 117
miles apart. A weather balloon is located on a
bearing of N 34°E from the western station and
on a bearing of N 13°E from the eastern station.
How far is the balloon from the western
station?
Solve the problem.
45) To find the distance between two small towns,
an electronic distance measuring (EDM)
instrument is placed on a hill from which both
towns are visible. If the distance from the EDM
to the towns is 4.8 miles and 3.7 miles and the
angle between the two lines of sight is 63°,
what is the distance between the towns?
Round your answer to the nearest tenth of a
mile.
46) A room in the shape of a triangle has sides of
length 12.6 yd, 15.7 yd, and 15.8 yd. If
carpeting costs $20.15 per sq. yd, padding costs
$2.50 per sq. yd, and there is no charge for
installation, how much, to the nearest dollar,
will it cost to carpet the room?
3
Answer Key
Testname: MATH 2412 TEST 2 REVIEW SPRING 2017
1)
6 cos + 1
cos - 1
24) 0, ,
2) -2 tan2
3) 0
4) cos3
25) 0,
5)
2( 3 - 1)
4
6)
2( 3 - 1)
4
7)
2( 3 - 1)
4
9)
1
2
24
10) 145
11)
38)
39)
44
125
40)
7
12)
25
13) -
336
625
14) -
5
5
15) -
10
10
16)
1
2
2-
2
17)
1
2
2+
2
18)
=
19)
=
20)
3
8
41)
+ 2k ,
+k ,
2
4
, ,
3
3
26) {30°, 150°}
27) {105°, 165°, 285°, 345°}
28) Yes
29) No
30) Yes
31) SSA; law of sines
32) SAS; law of cosines
33) C = 103°, a = 10.3 m, b = 18.3 m
34) a 7.3, B 7.8°, C 142.2°
35) A = 12.1°, C = 59.7°, c = 1227 cm
36) No solution
37) A1 = 30°, C1 = 127°, c1 = 33.54;
3
2
8)
3
2
42)
=
=
2
+ 2k
3
7
+k
8
A2 = 150°, C2 = 7°, c2 = 5.12
c = 14.8 km, A = 19.1°, B = 36.2°
A = 24.81°, B = 54.61°, C =
100.58°
The ambiguous case of the law
of sines occurs when we are
given the lengths of two sides of
an oblique triangle and the
measure of the angle opposite
one of them (a non-included
angle). In this case, it is possible
that 0, 1, or 2 triangles exist.
The law of sines requires that
we know either one side and
two angles or two sides and the
angle opposite one of them (a
non-included angle).
127 cm2
43) 14.7 in.2
44) 318 miles
45) 4.5 miles
46) $2060
2 7
7 13 5
,
,
,
,
,
12 6 3 12 6 12 3
,
,
19
12
21) 0
2
4
,
22)
3
3
23)
4