Download MAT 111 - Exam Review Questions Midterm Exam (#1

MAT 111 - Exam Review Questions
Midterm Exam (#1-44) and Final Exam (all)
Convert the angle in degrees to radians. Express answer
as a multiple of .
1) - 75°
Use a calculator to find the approximate value of the
expression. Round the answer to two decimal places.
9) cot 0.1433
Convert the angle in radians to degrees.
11
2)
12
Find the measure of the side of the right triangle whose
length is designated by a lowercase letter. Round your
answer to the nearest whole number.
10)
Find a positive angle less than 360° that is coterminal
with the given angle.
3) -822°
a
34°
b = 15
Find the length of the arc on a circle of radius r
intercepted by a central angle . Round answer to two
decimal places.
4) r = 15.26 inches, = 300°
Use a calculator to find the value of the acute angle
radians, rounded to three decimal places.
11) tan = 13.2894
Two sides of a right triangle ABC (C is the right angle)
are given. Find the indicated trigonometric function of
the given angle. Give an exact answer with a rational
denominator.
5)
Solve the problem.
12) A radio transmission tower is 190 feet tall.
How long should a guy wire be if it is to be
attached 13 feet from the top and is to make
an angle of 31° with the ground? Give your
answer to the nearest tenth of a foot.
9
Find csc .
A point on the terminal side of angle is given. Find the
exact value of the indicated trigonometric function of .
13) (-10, 24) Find sin .
4
is an acute angle and sin and cos are given. Use
identities to find the indicated value.
6) sin
=
11
, cos
6
in
=-
Find the exact value of the indicated trigonometric
function of .
9
in quadrant IV
Find tan .
14) sec = ,
8
5
. Find sec .
6
is an acute angle and sin is given. Use the
Pythagorean identity sin2 + cos2 = 1 to find cos .
1
7) sin =
4
15) cos
=
2
, sin
3
<0
Find tan .
Find the reference angle for the given angle.
16) -254°
Find a cofunction with the same value as the given
expression.
8) cos 11°
1
Use reference angles to find the exact value of the
expression. Do not use a calculator.
7
17) tan
6
23) y = -3 sin
1
x
3
The point P on the unit circle that corresponds to a real
number t is given. Find the values of the indicated
trigonometric function at t.
2
21
Find tan t.
18) ,
5 5
Determine the amplitude or period as requested.
1
19) Amplitude of y = - sin x
5
20) Period of y = -5 cos
1
x
4
24) y = 2 cos 3x +
2
-2
Determine the phase shift of the function.
1
21) y = sin (2x + )
2
Graph the function.
22) y = 2 sin (x -
2
)
Find the exact value of the expression.
25) sin-1 (-0.5)
26) cos-1 -
2
2
Use a sketch to find the exact value of the expression.
3
27) csc tan-1
3
2
Solve the right triangle shown in the figure. Round lengths
to one decimal place and express angles to the nearest
tenth of a degree.
Use the given information to find the exact value of the
expression.
5
and lies in
36) Find sin 2 if cos =
13
quadrant IV.
37) Find tan 2 if sin
=
7
and
25
lies in quadrant
II.
28) A = 35°, b = 54.8
Complete the identity.
29) csc x(sin x + cos x) = ?
A) -2 tan 2 x
C) sin x tan x
B) sec x csc x
Use the given information given to find the exact value of
the trigonometric function.
3
lies in quadrant IV
Find
39) sin = - ,
5
D) 1 + cot x
30) sin2 x + cot2 x + cos2 x = ?
A) sin3 x
C) csc2 x
31)
Write the expression as the sine, cosine, or tangent of a
double angle. Then find the exact value of the expression.
38) cos2 15° - sin2 15°
B) sec2 x
D) 2cos2 x
sin
.
Find all solutions of the equation.
40) 2 cos x + 2 = 0
1 - cos x
=?
sin x
A) csc x - cot x
C) csc x + cot x
B) csc x - cot x + 1
D) -csc x - cot x
Solve the equation on the interval [0, 2 ).
3
41) sin 4x =
2
Find the exact value by using a sum or difference
identity.
32) sin 75°
42) cos2 x + 2 cos x + 1 = 0
Find the exact value of the expression.
33) cos 50° cos 10° - sin 50° sin 10°
43) 2 cos2 x + sin x - 2 = 0
Use the given information to find the exact value of the
expression.
4
34) Find cos ( - ). sin = , lies in quadrant
5
II, and cos
2
=
2
,
5
Use a calculator to solve the equation on the interval
[0, 2 ). Round the answer to two decimal places.
44) sin x = -0.43
lies in quadrant I.
Find the exact value under the given conditions.
7
8
, 0 < < ; cos =
, 0<
35) sin =
25
2
17
<
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree.
45) B = 26°
C = 115°
b = 49
2
Find tan ( + ).
3
57) r = -9 cos
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.
46) B = 15°, b = 10.7, a = 13.78
The graph of a polar equation is given. Select the polar
equation for the graph.
58)
Find the area of the triangle having the given
measurements. Round to the nearest square unit.
47) B = 25°, a = 4 feet, c = 9 feet
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree.
48) a = 8, c = 12, B = 126°
49) a = 8, b = 6, c = 4
A) r = -2 sin
C) r sin = -1
Solve the problem.
50) Two airplanes leave an airport at the same
time, one going northwest (bearing N45°W) at
420 mph and the other going east at 348 mph.
How far apart are the planes after 2 hours (to
the nearest mile)?
B) r = -1
D) r = -2 cos
Use a graphing utility to graph the polar equation.
59) r = cos 4
Use Heron's formula to find the area of the triangle.
Round to the nearest square unit.
51) a = 21 yards, b = 18 yards, c = 14 yards
Find another representation, (r, ), for the point under the
given conditions.
52) 3,
3
, r < 0 and 0 <
<2
Polar coordinates of a point are given. Find the
rectangular coordinates of the point.
53) (9, 120°)
Use the given vectors to find the specified scalar.
60) u = -14i + 10j and v = -15i - 13j; Find u · v.
Find the angle between the given vectors. Round to the
nearest tenth of a degree.
61) u = i - j, v = 3i + 5j
The rectangular coordinates of a point are given. Find
polar coordinates of the point.
54) (-3, 0)
Find the absolute value of the complex number.
62) z = 6 - 15i
Convert the rectangular equation to a polar equation that
expresses r in terms of .
55) x2 + y2 = 25
Write the complex number in polar form. Express the
argument in radians.
63) 5 - 5i
Convert the polar equation to a rectangular equation.
5
56) =
6
4
Write the complex number in rectangular form.
64) 3(cos 225° + i sin 225°)
Graph the ellipse and locate the foci.
75) 9x 2 + 16y2 = 144
Find the product of the complex numbers. Leave answer
in polar form.
65) z1 = 2(cos 37° + i sin 37°)
z2 = 7(cos 14° + i sin 14°)
Find the quotient
z1
z2
of the complex numbers. Leave
answer in polar form.
3
3
)
+ i sin
66) z1 = 6(cos
2
2
z2 = 12(cos
5
5
+ i sin
)
6
6
Graph the ellipse.
(x + 1)2 (y + 2)2
+
=1
76)
9
16
Use DeMoivre's Theorem to find the indicated power of
the complex number. Write answer in rectangular form.
67) 4(cos 15° + i sin 15°) 4
Find all the complex roots. Write the answer in polar
form.
68) Cube roots of 27(cos 279° + i sin 279°)
Find the magnitude v
69) v = -5i + 2j
of the vector.
A vector v has initial point P1 and terminal point P2 .
Write v in terms of ai + bj.
70) P1 = (-6, 3); P2 = (1, -2)
Find the standard form of the equation of the ellipse
satisfying the given conditions.
77) Foci: (0, -5), (0, 5); vertices: (0, -8), (0, 8)
Find the specified vector or scalar.
71) u = -7i - 2j, v = 4i + 7j; Find u - v.
Find the standard form of the equation of the ellipse and
give the location of its foci.
78)
Solve the problem.
72) A child throws a ball with a speed of 7 feet
per second at an angle of 66° with the
horizontal. Express the vector described in
terms of i and j. If exact values are not
possible, round components to 3 decimals.
Use the given vectors to find the specified scalar.
73) u = 13i + 10j and v = 5i + 10j; Find u · v.
Find the angle between the given vectors. Round to the
nearest tenth of a degree.
74) u = i - j, v = 2i + 6j
5
Find the vertices and locate the foci for the hyperbola
whose equation is given.
y2 x 2
=1
79)
9
16
Find the standard form of the equation of the parabola
using the information given.
85) Focus: (15, 0); Directrix: x = -15
86) Vertex: (3, -4); Focus: (3, -2)
Find the standard form of the equation of the hyperbola
satisfying the given conditions.
80) Foci: (-10, 0), (10, 0); vertices: (-4, 0), (4, 0)
Find the vertex, focus, and directrix of the parabola with
the given equation.
87) (y - 2)2 = -20(x - 4)
Find the standard form of the equation of the hyperbola.
81)
Graph the parabola with the given equation.
88) (y - 1)2 = 7(x - 1)
Find the location of the center, vertices, and foci for the
hyperbola described by the equation.
(x - 3)2 (y + 2)2
=1
82)
25
16
Identify the equation without completing the square.
89) 4x 2 - 4x + y - 2 = 0
90) 2x 2 + 4y2 + 4x + 4y = 0
Use the center, vertices, and asymptotes to graph the
hyperbola.
(y - 1)2 (x - 2)2
=1
83)
4
9
91) y2 - 2x 2 + 2x + 4y + 1 = 0
Parametric equations and a value for the parameter t are
given. Find the coordinates of the point on the plane
curve described by the parametric equations
corresponding to the given value of t.
92) x = t3 + 1, y = 7 - t4; t = 2
Eliminate the parameter t. Find a rectangular equation for
the plane curve defined by the parametric equations.
93) x = 3t, y = t + 2; -2 t 3
Find the focus and directrix of the parabola with the
given equation.
84) x2 = -4y
6