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A
Absolute value of a complex number, 158
Accuracy of computed results, 28, 44
Acute angle, functions of, 26
Addition formulas, 94
Addition of vectors, 54
Airspeed of airplane, 56
Ambiguous case of law of, sines, 112, 113, 114
Amplitude of a complex number, 158
of sine curve, 77
complementary, functions of, 27
first quadrant, 11
double, functions of, 94
of elevation, 30
general, functions of, 12
measure of, degree, 2
measure of, radian, 2
negative, 1
positive, 1
quadrantal, 12
functions of, 13
reference, 67
standard positions of, 11
Angles, 168
Angular velocity, 5
Arc length, 3
on a unit circle, 4
Area:
of circular segment, 134
B
Basic relationships, 86
cofunction, 27
negative angle, 66
Bearing, 53
C
Calculator, use of, 28, 42, 43, 44
Circles, 172
Circular functions, 15
Cis θ, 158
Cofunction, 27
Complementary angles, functions of, 27
Complex numbers, 156
absolute value of, 158
amplitude of, 158
conjugate of, 156
graphic representation of, 157
modulus of, 158
product and quotient of, 159
rectangular form of, 157
trigonometric form of, 157, 158
Components of a vector, 56
Composition of sine curves, 78, 79
Conditional equations, 147
Conjugate complex numbers, 156
Conjugate expressions, 88
Conversion formulas for degree, and radian measure, 2
Coordinates, rectangular, 10
Cosecant, defined, 27
graph of, 76
line representation of, 74, 75
period of, 77
graph of, 76
line representation of, 74, 75
period of, 77
graph of, 76
line representation of, 74, 75
period of, 77
Course, 56
D
Degree, 2
De Moivre’s theorem, 159
Difference of complex numbers, 156
Difference of two angles, formulas, 94
Digits, significant, 44
Directed distance, 10
Directed line, 10
Distance of a point, 11
Double-angle formulas, 94
Drift angle of airplane, 56
E
Elevation, angle of, 30
Equations, trigonometric, 147
inverse trigonometric, 138
Error in computed results, 28, 44
F
Figures, significant, 44
Formulas:
conversion, degree and radian, 2
difference of two angles, 94
double-angle, 94
half-angle, 95
Heron’s, 129
product to sum, 106
sum of two angles, 94
sum to product, 106
Functions, inverse trigonometric, 138, 139
Functions, trigonometric:
of acute angles, 26
basic relations among, 12, 27, 66, 86
of complementary angles, 27
of difference of two angles, 94
of double-angles, 94
of general angle, 12
graphs of, 76
of half-angle, 95
line representations of, 74, 75
of negative angles, 66
of sum of two angles, 94
signs of, 13
variations of, 75
Fundamental period, 77
G
General angle, functions of, 12
General values of inverse relations, 140
Graphs:
of inverse functions, 139
of inverse relations, 138, 139
of trigonometric functions, 76
Ground speed of airplane, 56
H
Half-angle formulas, 95
Heading of airplane, 56
Heron’s formula, 129
Horizontal shift, 76
Hypotenuse, 26
I
Identities, trigonometric, 87, 147
of cofunction, 27
negative angle, 66
Imaginary unit, 156
Initial side, 1
Interpolation in tables, 40, 41, 42
Inverse notation, 138
Inverse trigonometric functions, 138, 139
domain of, 139
graphs of, 139
principal-value range, 140
Inverse trigonometric relations, 138
graphs of, 139
L
Length of an arc, 3
on a unit circle, 4
Line representations of functions, 74, 75
Linear velocity, 5
Lines, 169
M
Magnitude of a vector, 54
Measure of an angle, 2
Minute, 2
Modulus of a complex number, 158
Multiplication of complex numbers, 156, 159
N
Negative angle, 1
trigonometric functions of, 66
Number scale, 10
O
Oblique triangle, 110
Origin, 10
P
Parallelogram law for vector addition, 55, 157, 158
Plane trigonometry, 1
Polar form of complex number, 157, 158
Polygons, 171
Positive angle, 1
Powers of complex number, 159
Principal-value of inverse functions, 140
Product to sum formulas, 106
Pythagorean relationships, 86
Q
Quadrantal angles, 12
functions of, 13
Quadrants, 11
Quadrant signs of functions, 11
Quotient of two complex numbers, 157, 158
Quotient relationships, 86
R
Radian, 2
Radius vector of a point, 11
Range, principal-value, 140
Reciprocal relationships, 12, 86
Rectangular coordinates, 10
Rectangular form, 158
Reference angle, 67
Relations, inverse trigonometric, 138, 140
Resultant of two vectors, 54, 55
Right triangle, solution of, 27
Roots of a complex number, 160
Rounding-off procedures, 28, 44
S
graph of, 76
line representation of, 74, 75
period of, 77
Second, 2
Sector of a circle, 5
Shifts, vertical and horizontal, 76
Side:
adjacent, 26
hypotenuse, 26
initial, 1
opposite, 26
terminal, 1
Sides of an angle, 1
Significant digits, 44
Signs of trigonometric functions, 13
graph of, 76
line representation of, 74, 75
period of, 77
Sine curve, composition of, 79, 81
Sines, law of, 110
Solving trigonometric equations, 139, 140
Speed, 56
Standard position of a trigonometric angle, 11
Subtend, 2
Subtraction formulas, 94
Sum
of complex numbers, 156
of vectors, 54
Sum formulas, 94
Sum to product formulas, 106
T
Tables of trigonometric function values, 28, 39
graph of, 76
line representations of, 74, 75
period of, 77
Tangents to a circle, 172
Terminal side, 1
Triangle
oblique, 110
right, 26
Triangle methods of vector addition, 55
Trigonometric equations, 147
Trigonometric form of complex number, 157, 158
Trigonometric functions
applications of, 1
of acute angles, 27
of difference of two angles, 94
of double-angle, 94
fundamental relations among, 12, 27, 66, 86
of general angle, 12
graphs of, 76
of half-angle, 95
line representations of, 74
of negative angle, 66
of quadrantal angles, 13
of sum of two angles, 94
variations of, 75
Trigonometric identities, 12, 27, 66, 86, 87, 89, 94, 95, 106
Trigonometry, 1
U
Unit circle, 4
Undefined trigonometric functions, 13, 14
V
Variations of functions, 75
Vector direction, 54
Vector quantity, 54
Vectors, 54
Velocity, 5
Vertical shift, 76
Vertex of an angle, 1
W
Wind speed, 56