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MAC 1114 - Trigonometry Review for Chapter 6
Section 6.1-6.5
Please note this review does not reflect all types of questions that may be asked on an exam.
Solve the problem.
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree.
10) 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)?
1) A = 26°
B = 23°
a = 49.8
Solve the triangle.
2)
75°
11) 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?
7
Use Heron's formula to find the area of the triangle.
Round to the nearest square unit.
50°
12) a = 12 meters, b = 18 meters, c = 7 meters
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.
Match the point in polar coordinates with either A, B, C,
or D on the graph.
13) (-2, -
3) B = 28°, b = 18.4, a = 19.6
4) B = 31°, b = 14, a = 26
5) A = 30°, a = 22, b = 44
Find the area of the triangle having the given
measurements. Round to the nearest square unit.
6) B = 10°, a = 4 feet, c = 7 feet
Solve the problem.
7) To find the distance AB across a river, a
distance BC of 1221 m is laid off on one side of
the river. It is found that B = 110.8° and
C = 13.7°. Find AB. Round to the nearest
meter.
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree.
8) a = 8, b = 14, c = 16
9) b = 4, c = 6, A = 75°
1
2
)
Use a polar coordinate system to plot the point with the
given polar coordinates.
3
)
14) (-2,
4
24)
=
5
6
The graph of a polar equation is given. Select the polar
equation for the graph.
25)
Find another representation, (r, ), for the point under the
given conditions.
15) 9,
16) 1,
3
4
, r > 0 and -2
<
A) r = 2 sin
B) r sin
=1
C) r = 1
D) r = 2 cos
<0
Test the equation for symmetry with respect to the given
axis, line, or pole.
, r < 0 and 0 <
26) r = 2 cos ; the polar axis
<2
27) r = 6 + 2 sin ; the line
Polar coordinates of a point are given. Find the
rectangular coordinates of the point.
17) (-3, 120°)
Graph the polar equation.
28) r = 6 sin
18) (3, 270°)
The rectangular coordinates of a point are given. Find
polar coordinates of the point.
19) (6 3, 6)
20) (-4 2, -4 2)
Convert the rectangular equation to a polar equation that
expresses r in terms of .
21) (x - 3)2 + y2 = 9
22) y = 3
Convert the polar equation to a rectangular equation.
23) r = -3 cos
2
=
2
29) r = 1 + sin
Plot the complex number.
30) r = 3 sin 2
Find the absolute value of the complex number.
32) -3 + 6i
33) z = -14 - 8i
Write the complex number in polar form. Express the
argument in degrees.
34) 2i
Write the complex number in polar form. Express the
argument in radians.
35) 4 - 4i
Write the complex number in rectangular form.
36) 9.67(cos 155.2° + i sin 155.2°)
31) r cos
= -2
Find the product of the complex numbers. Leave answer
in polar form.
37) z1 = 5(cos 20° + i sin 20°)
z2 = 4(cos 10° + i sin 10°)
Find the quotient
z1
of the complex numbers. Leave
z2
answer in polar form.
38) z1 = 8(cos
2
z2 = 3(cos
6
+ i sin
+ i sin
2
6
)
)
Use DeMoivre's Theorem to find the indicated power of
the complex number. Write answer in rectangular form.
39) 4(cos 15° + i sin 15°) 4
40) (1 + i) 20
3
Find all the complex roots. Write the answer in the
indicated form.
41) The complex cube roots of 216(cos 135° + i sin
135°) (polar form)
42) The complex square roots of 2 (cos
2
+ i sin
3
2
) (rectangular form)
3
4