Download MTH 113 test 2 practice summer 2013.tst

MTH 13 Test 2 Practice Problems
Summer 2013
Working on one side only, verify the given identity.
sin x cos x
1)
+
=sec x csc x
cos x sin x
11) tan α =
< π Find tan (α + β).
Use the given information to find the exact value of the
expression.
7
12) Find cos 2θ. sin θ =
, θ lies in quadrant I.
25
2) csc2 x sec x = sec x + csc x cot x
Find the exact value of the expression.
3) cos (245° - 5°)
Use the given information to find the exact value of the
expression.
4
4) Find cos (α - β). sin α = , α lies in quadrant
5
II, and cos β =
2
, β lies in quadrant I.
5
Use the given information to find the exact value of the
expression.
15
7) Find sin (α + β).
tan α =
, α lies in
8
4
, θ lies in quadrant II.
5
Use the given information given to find the exact value of
the trigonometric function.
3
18) cos θ = - ,
θ lies in quadrant III
Find
5
quadrant II.
quadrant III, and sin β =
14) Find tan 2θ. sin θ =
Use a half-angle formula to find the exact value of the
expression.
5π
17) sin
12
7
, β lies in
25
cos α = -
21
, θ lies in quadrant III.
20
Use a half-angle formula to find the exact value of the
expression.
16) cos 112.5°
Find the exact value of the expression.
6) sin 25° cos 35° + cos 25° sin 35°
8) Find cos (α + β).
13) Find sin 2θ. tan θ =
Write the expression as the sine, cosine, or tangent of a
double angle. Then find the exact value of the expression.
15) cos2 120° - sin2 120°
Find the exact value by using a sum or difference identity.
5) sin 15°
quadrant III, and cos β = -
24
3π
20 π
, π<α<
; cos β = ,
<β
7
2
29 2
7
, α lies in
25
21
, β lies in
5
cos
quadrant II.
θ
.
2
Find all solutions of the equation.
19) 2 cos x + 2 = 0
Find the exact value by using a difference identity.
9) tan 75°
20) 8 sin x + 6 2 = 6 sin + 5 2
Find the exact value under the given conditions.
3
π
20
π
10) sin α = , 0 < α < ; cos β =
, 0<β<
5
2
29
2
Solve the equation on the interval [0, 2π).
3
21) sin 4x =
2
Find tan (α + β).
1
22) cos 2x =
Two sides and an angle (SSA) of a triangle are given.
Determine whether the given measurements produce one
triangle, two triangles, or no triangle at all. Solve each
triangle that results. Round lengths to the nearest tenth
and angle measures to the nearest degree.
36) A = 30°, a = 22, b = 44
3
2
23) cos2 x + 2 cos x + 1 = 0
24) cos x = sin x
37) B = 114°, b = 4, a = 25
25) sec2 x - 2 = tan2 x
38) B = 28°, b = 18.4, a = 19.6
26) sin2 x + sin x = 0
39) B = 41°, a = 4, b = 3
Solve the equation on the interval [0, 2π).
27) (tan x + 1) (cos x + 1) = 0
Find the area of the triangle having the given
measurements. Round to the nearest square unit.
40) A = 30°, b = 15 inches, c = 5 inches
28) sin x - 2 sin x cos x = 0
41) A = 20°, b = 17 meters, c = 7 meters
Solve the equation on the interval [0, 2π).
29) cos 2x = 2 - cos 2x
Solve the problem.
42) A guy wire to a tower makes a 70° angle with
level ground. At a point 38 ft farther from the
tower than the wire but on the same side as the
base of the wire, the angle of elevation to the
top of the tower is 37°. Find the length of the
wire (to the nearest foot).
30) sin 2x + sin x = 0
31) 2 cos2 x + sin x - 2 = 0
Use a calculator to solve the equation on the interval [0, 2
π). Round to the nearest hundredth.
32) sin 2x + sin x = 0
Find a. If necessary, round your answer to two decimal
places.
43)
Solve the triangle.
33)
75°
7
45°
25°
50°
1.8
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree.
34) B = 30°
C = 111°
b = 33
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree.
44)
9
6
35) A = 11.2°, C = 131.6°, a = 91.2
4
2
45) a = 6, b = 9, C = 115°
46) a = 8, b = 14, c = 16
Solve the problem.
47) Two airplanes leave an airport at the same
time, one going northwest (bearing 135°) at 409
mph and the other going east at 325 mph. How
far apart are the planes after 4 hours (to the
nearest mile)?
48) A painter needs to cover a triangular region 60
meters by 69 meters by 70 meters. A can of
paint covers 70 square meters. How many
cans will be needed?
Use Heron's formula to find the area of the triangle.
Round to the nearest square unit.
49) a = 16 yards, b = 13 yards, c = 16 yards
Without using a calculator, find the exact value.
π
50) sec
4
51) sin (-
π
)
6
52) cot -
π
2
53) cos
5π
4
54) sin
11π
3
55) cos
35π
6
3
Answer Key
Testname: MTH 113 TEST 2 PRACTICE SUMMER 2013
1) Working on the left side:
sin x sin x cos x cos x
·
+
·
cos x sinx sin x cos x
18) -
sin2 x
cos2 x
+
cos x sin x sin xc cos x
sin2 x + cos2 x
cos x sin x
1
cos x sin x
1
1
·
cos x sin x
8)
16) -
1
2
17)
1
2
π
5π
, π,
3
3
π 7π 9π 15π
,
,
,
8 8
8
8
2π
4π
, π,
3
3
π 5π
,
6 6
A2 = 119°, C2 = 20°, c2 = 1.6
40) 19 square inches
41) 20 square meters
42) 42 feet
43) 2.22
44) A = 127.2°, B = 32.1°, C = 20.7°
45) c = 12.8, A = 25°, B = 40°
46) A = 30°, B = 61°, C = 89°
47) 2716 miles
48) 27 cans
49) 95 square yards
24
14)
7
1
2
3π
7π
, π,
4
4
A2 = 150°, C2 = 2°, c2 = 1.4
39) A1 = 61°, C1 = 78°, c1 = 4.5;
840
13)
841
15) -
π 11π 13π 23π
,
,
,
12 12 12 12
32) 0, 2.09, 3.14, 4.19
33) B = 55°, a = 6.55, c = 8.25
34) A = 39°, a = 41.5, c = 61.6
35) B = 37.2°, b = 283.9, c = 351.1
36) B = 90°, C = 60°, c = 38.1
37) no triangle
38) A1 = 30°, C1 = 122°, c1 = 33.2;
3+2
144
10)
17
527
625
22)
31) 0, π,
9)
12)
π π 2π 7π 7π 13π 5π 19π
, ,
,
,
,
,
,
12 6 3 12 6 12 3
12
30) 0,
14 + 24 21
125
333
644
21)
29)
87
425
11)
5π
7π
+ 2nπ or x =
+ 2nπ
4
4
28) 0,
3
2
7) -
20) x =
27)
2( 3 - 1)
4
6)
3π
5π
+ 2nπ or x =
+ 2nπ
4
4
25) no solution
3π
26) 0, π,
2
-6 + 4 21
25
5)
19) x =
23) π
π 5π
24) ,
4 4
sec x csc x
2) Pick a side and simplify until it looks like the other
side.
1
3) 2
4)
5
5
22+
2
3
4
Answer Key
Testname: MTH 113 TEST 2 PRACTICE SUMMER 2013
50)
2
1
51) 2
52) 0
53) -
2
2
54) -
3
2
55)
3
2
5