[Math] McGraw-Hill - Teach Yourself Trigonometry (1992).pdf

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Contents
Introduction
1
Geometrical Foundations
The nature of geometry. Plane surfaces. Angles
and
their measurement. Geometrical theorems; lines
and triangles. Quadrilaterals. The circle. Solid
geometry. Angles of elevation and depression.
2 Using your Calculator
Arithmetic and algebraic calculators. Rounding or
truncating calculators. Differing calculator displays.
Using your calculator for simple calculations. The
clear keys. Handling minus signs and negative
numbers. Calculations involving brackets. Using the
memory. Using other mathematical functions.
Functions and their inverses. Changing degrees to
degrees, minutes and seconds. Changing degrees to
radians. Finding trigonometrical functions. Finding
inverse trigonometrical functions.
3
The Trigonometrical Ratios
The tangent. Changes of tangents in the first
quadrant. Tables of tangents. Uses of tangents. The
sine and cosine. Changes of sines and cosines in the
first quadrant. Uses of sines and cosines. The
cosecant, secant and cotangent. Using your
ratios. Graphs
calculator for other trigonornetr~cal
of trigonometrical ratios. Uses of other
trigonometrical ratios. Solution of right-angled
triangles. Slope and gradient. Projections.
VIII
...
1
28
VI
Contents
4
Relations between the Trigonometrical Ratios
tan
0
=
-
sln
0
s~n'0
cos
0
+
cos'
0
=
1
tan'
0
1
=
sec'
0
cot'
0
+
1
=
cosec'
0
5
Ratios of Angles in the Second Quadrant
Pos~t~ve negatlve l~nes
and
D~rect~on rotatlon of angle
of
The slgn
convention
for the hypotenuse
To find the ratlo of angles In the second
quadrant
from the tables
To find an angle when a ratlo
IS
glven
The Inverse notatlon
Grdphs of the slne, c o m e and tangent between 0"
dnd 360"
6
Trigonometrical Ratios of Compound Angles
sln
(A
+
B)
=
sln
A
cos
B
+
cos
A
sln B, etc
sln
(A
-
B)
=
sln
A
cos B
-
cos
A
sln B, etc
tan
(A
B) and tan
(A
-
B) Mult~ple
and sub-
mult~ple
formulae Product formulae
7
Relations between the Sides and Angles of a Triangle
The slne rule The c o m e rule The half-angle
+
87
+
100
A
formulae Formula for sln
-
In terms of the s~des
2
A
Formula for cos
-
In terms of the s~des
2
A
Formula for tan
-
In terms of the s~des
2
Formula for sln
A
In terms of the s~des
tan
-
b -
-
A
B-C-
-
ccot
2
b+c
2
a=bcos~+c cos~
8
The Solution of Triangles
114
Case
I
Three s~des
known Case
I1
Two s~des
and
conta~ned
angle known Case
111
Two angles and a
s~de
known Case
IV
The amb~guou\
case The
area of a tr~angle
9
Practical problems involving the Solution of
127
Triangles
D e t e r ~ i l ~ n ? 'ofm he~ght a d~sldnt
~ the
of
object
Contents
Distance of an lnaccesslble object D~stance
between two vlslble but lnaccess~ble
objects
Trlangulat~onWorked examples
10
Circular Measure
Ratlo of
circumference
of a c~rcle ~ t d~ameter
to
s
The radlan To find the c~rcular
measure of an
angle The length of an arc
11
Trigonometrical Ratios of Angles of any Magnitude
Angles In the 3rd dnd 4th quadrants
Variations
In the sine between
0"
and 360"
Varlat~ons the c o m e between
0
and 360"
In
"
Varlat~ons the tangent between
0"
and 360"
In
Ratlos of angles greater than 360"
Ratios of
(-
0)
Ratlos of
0
and
(180"
0)
Ratios of
0
and (360"
-
0)
Angles wlth glven tr~gonometr~cal
ratlos
12
Trigonometrical Equations
Types of
equations
The form a cos
0
-
b sin
0
=
c
VII
141
147
+
Summary of Trigonometrical Formulae
Tables
A n s ers
~

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