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

MAT 111 - Exam Review Questions
Midterm Exam (#1-43) 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. Round to two
decimal places.
2) 2 radians
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 .
4
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 .
is an acute angle and sin and cos are given. Use
identities to find the indicated value.
11
5
, cos = - . Find sec .
6) sin =
6
6
Find the exact value of the indicated trigonometric
function of .
9
in quadrant IV
Find tan .
14) sec = ,
8
is an acute angle and sin is given. Use the Pythagorean
identity sin2 + cos2 = 1 to find cos .
7) sin
=
in
Find the reference angle for the given angle.
15) -254°
1
4
Use reference angles to find the exact value of the
expression. Do not use a calculator.
7
16) tan
6
Find a cofunction with the same value as the given
expression.
8) cos 11°
1
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.
17) ,
5 5
23) y = 2 cos 3x +
2
-2
Determine the amplitude or period as requested.
1
18) Amplitude of y = - sin x
5
19) Period of y = -5 cos
1
x
4
Determine the phase shift of the function.
1
20) y = sin (2x + )
2
Find the exact value of the expression.
24) sin-1 (-0.5)
Graph the function.
21) y = 2 sin (x -
2
)
25) cos-1 -
2
2
Use a sketch to find the exact value of the expression.
3
26) csc tan-1
3
Solve the right triangle shown in the figure. Round lengths
to one decimal place and express angles to the nearest
tenth of a degree.
22) y = -3 sin
1
x
3
27) A = 35°, b = 54.8
Complete the identity.
28) csc x(sin x + cos x) = ?
A) -2 tan2 x
C) sin x tan x
B) sec x csc x
D) 1 + cot x
29) sin2 x + cot2 x + cos2 x = ?
A) sin3 x
B) sec2 x
2
C) csc x
D) 2cos2 x
2
Solve the equation on the interval [0, 2 ).
3
40) sin 4x =
2
1 - cos x
=?
30)
sin x
A) csc x - cot x
C) csc x + cot x
B) csc x - cot x + 1
D) -csc x - cot x
41) cos2 x + 2 cos x + 1 = 0
Find the exact value by using a sum or difference identity.
31) sin 75°
42) 2 cos2 x + sin x - 2 = 0
Find the exact value of the expression.
32) cos 50° cos 10° - sin 50° sin 10°
Use a calculator to solve the equation on the interval
[0, 2 ). Round the answer to two decimal places.
43) sin x = -0.43
Use the given information to find the exact value of the
expression.
4
33) Find cos ( - ). sin = , lies in quadrant
5
II, and cos
=
2
,
5
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree.
44) B = 26°
C = 115°
b = 49
lies in quadrant I.
Find the exact value under the given conditions.
7
8
, 0 < < ; cos =
, 0<
34) sin =
25
2
17
<
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.
45) B = 15°, b = 10.7, a = 13.78
2
Find tan ( + ).
Use the given information to find the exact value of the
expression.
5
and lies in
35) Find sin 2 if cos =
13
Find the area of the triangle having the given
measurements. Round to the nearest square unit.
46) B = 25°, a = 4 feet, c = 9 feet
quadrant IV.
36) Find tan 2 if sin
=
7
and
25
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree.
47) a = 8, c = 12, B = 126°
lies in quadrant
II.
Write the expression as the sine, cosine, or tangent of a
double angle. Then find the exact value of the expression.
37) cos2 15° - sin2 15°
48) a = 8, b = 6, c = 4
Solve the problem.
49) 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)?
Use the given information given to find the exact value of
the trigonometric function.
3
lies in quadrant IV
Find
38) sin = - ,
5
sin
2
.
Use Heron's formula to find the area of the triangle.
Round to the nearest square unit.
50) a = 21 yards, b = 18 yards, c = 14 yards
Find all solutions of the equation.
39) 2 cos x + 2 = 0
3
Find another representation, (r, ), for the point under the
given conditions.
51) 3,
3
, r < 0 and 0 <
Use a graphing utility to graph the polar equation.
58) r = cos 4
<2
Polar coordinates of a point are given. Find the rectangular
coordinates of the point.
52) (9, 120°)
The rectangular coordinates of a point are given. Find
polar coordinates of the point.
53) (-3, 0)
Convert the rectangular equation to a polar equation that
expresses r in terms of .
54) x2 + y2 = 25
Use the given vectors to find the specified scalar.
59) u = -14i + 10j and v = -15i - 13j; Find u · v.
Convert the polar equation to a rectangular equation.
5
55) =
6
Find the angle between the given vectors. Round to the
nearest tenth of a degree.
60) u = i - j, v = 3i + 5j
Find the absolute value of the complex number.
61) z = 6 - 15i
56) r = -9 cos
The graph of a polar equation is given. Select the polar
equation for the graph.
57)
Write the complex number in polar form. Express the
argument in radians.
62) 5 - 5i
Write the complex number in rectangular form.
63) 3(cos 225° + i sin 225°)
Find the product of the complex numbers. Leave answer in
polar form.
64) z1 = 2(cos 37° + i sin 37°)
z2 = 7(cos 14° + i sin 14°)
A) r = -2 sin
C) r sin = -1
Find the quotient
B) r = -1
D) r = -2 cos
z1
z2
of the complex numbers. Leave
answer in polar form.
3
3
+ i sin
)
65) z1 = 6(cos
2
2
z2 = 12(cos
5
5
+ i sin
)
6
6
Use DeMoivre's Theorem to find the indicated power of
the complex number. Write answer in rectangular form.
66) 4(cos 15° + i sin 15°) 4
4
Find the standard form of the equation of the ellipse
satisfying the given conditions.
74) Foci: (0, -5), (0, 5); vertices: (0, -8), (0, 8)
Find all the complex roots. Write the answer in polar form.
67) Cube roots of 27(cos 279° + i sin 279°)
Find the magnitude v of the vector.
68) v = -5i + 2j
Find the standard form of the equation of the ellipse and
give the location of its foci.
75)
A vector v has initial point P1 and terminal point P2. Write
v in terms of ai + bj.
69) P1 = (-6, 3); P2 = (1, -2)
Find the specified vector or scalar.
70) u = -7i - 2j, v = 4i + 7j; Find u - v.
Solve the problem.
71) 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.
Find the vertices and locate the foci for the hyperbola
whose equation is given.
y2 x2
=1
76)
9
16
Graph the ellipse and locate the foci.
72) 9x2 + 16y2 = 144
Find the standard form of the equation of the hyperbola
satisfying the given conditions.
77) Foci: (-10, 0), (10, 0); vertices: (-4, 0), (4, 0)
Find the standard form of the equation of the hyperbola.
78)
Graph the ellipse.
(x + 1)2 (y + 2)2
+
=1
73)
9
16
Find the location of the center, vertices, and foci for the
hyperbola described by the equation.
(x - 3)2 (y + 2)2
=1
79)
25
16
5
Use the center, vertices, and asymptotes to graph the
hyperbola.
(y - 1)2 (x - 2)2
=1
80)
4
9
87) 2x2 + 4y2 + 4x + 4y = 0
88) 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.
89) 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.
90) x = 3t, y = t + 2; -2 t 3
Find the focus and directrix of the parabola with the given
equation.
81) x2 = -4y
Find the standard form of the equation of the parabola
using the information given.
82) Focus: (15, 0); Directrix: x = -15
83) Vertex: (3, -4); Focus: (3, -2)
Find the vertex, focus, and directrix of the parabola with
the given equation.
84) (y - 2)2 = -20(x - 4)
Graph the parabola with the given equation.
85) (y - 1)2 = 7(x - 1)
Identify the equation without completing the square.
86) 4x2 - 4x + y - 2 = 0
6