Using your calculator 28 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. Changing degrees to degrees, minutes and seconds. Finding inverse trigonometrical functions. Solution of right-angled triangles. Slope and gradient. Projections.
Using your calculator 28 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. Changing degrees to degrees, minutes and seconds. Finding inverse trigonometrical functions. Solution of right-angled triangles. Slope and gradient. Projections.
Using your calculator 28 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. Changing degrees to degrees, minutes and seconds. Finding inverse trigonometrical functions. Solution of right-angled triangles. Slope and gradient. Projections.
Using your calculator 28 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. Changing degrees to degrees, minutes and seconds. Finding inverse trigonometrical functions. Solution of right-angled triangles. Slope and gradient. Projections.
Copyright:
Attribution Non-Commercial (BY-NC)
Available Formats
Download as PDF, TXT or read online from Scribd
Download as pdf or txt
You are on page 1of 198
Contents
Introduction
1 Geometrical Foundations 1
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 28
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 39
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
calculator for other trigonometrical ratios. Graphs
of trigonometrical ratios. Uses of other
trigonometrical ratios. Solution of right-angled
triangles. Slope and gradient. Projections.vi Contents
4 Relations between the Trigonometrical Ratios
tan 9 = 2 8
cos 8
tan? 6 + 1 = sec’ 6
cot? @ + 1 = cosec’ 6
5 Ratios of Angles in the Second Quadrant
Positive and negative lines
Direction of rotation of angle
The sign convention for the hypotenuse
To find the ratio of angles in the second quadrant
from the tables
To find an angle when a ratio 1s given
The inverse notation
Graphs of the sine, cosine and tangent between 0°
and 360°
6 Trigonometrical Ratios of Compound Angles
sin (A + B) = sin Acos B + cos A sin B, ete
sin (A — B) = sin Acos B — cos A sin B, etc
tan (A + B) and tan (A — B) Multiple and sub-
multiple formulae Product formulae
7 Relations between the Sides and Angles of a Triangle
The sine rule The cosine rule The half-angle
sin? 6 + cos" 6 = 1
formulae Formula for sin 4 in terms of the sides
A
Formula for cos 7 in terms of the sides
Formula for tan $ 1n terms of the sides
Formula for sin A in terms of the sides
tan BSE = PZ co 4 a= bcos C + ccosB
8 The Solution of Triangles
Case I Three sides known Case II Two sides and
contained angle known Case III Two angles and a
side known Case IV The ambiguous case The
area of a triangle
9 Practical problems involving the Solution of
Triangles
Deteriaina'ion of the height of a disiant object
72
75
87
100
114
127