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## Has done two years of high school algebra and geometry

In the government school system, that's the first three years of high school math.

The fourth (and last) year will be covered with

Life of Fred: Trigonometry Expanded Edition

This book covers what is often called pre-calculus.

This hardback book will do three things:

1. Offer a complete course in trig, including:

Sines

angle of elevation

opposite and hypotenuse

definition of sine

angle of depression

area of a triangle (A = ½ ab sin θ)

Cosines and Tangents

adjacent side

slope and tan θ

tan 89.999999999999999999999º

solving triangles

Trig Functions of Any Angle

initial and terminal sides of an angle

standard position of an angle

coterminal angles

expanding the domain of a function

periodic functions

cosine is an even function

sine is an odd function

Trig Identities

definition of an identity

proving identities

four suggestions for increasing your success in proving identities

cotangent, secant and cosecant

cofunctions of complementary angles

eight major tricks to prove identities

Radian Measurement

degrees, minutes, seconds

sectors

conversions between degrees and radians

area of a sector (A = ½ r²θ)

Conditional Trig Equations and Functions of Two Angles

definition of a conditional equation

addition formulas

double-angle formulas

half-angle formulas

sum and difference formulas

product formulas

powers formulas

Oblique Triangles

law of sines

law of cosines

Inverse Trig Functions

using a calculator to find trig inverses

principal values of the arctan, arcsin and arccosine

the ambiguous case

Polar Coordinates

Cartesian coordinates

graph polar equations

converting between Cartesian and polar coordinates

the polar axis and the pole

symmetry with respect to a point and with respect to a line

Polar Form of Complex Numbers

r cis θ means r(cos θ + i sin θ)

de Moivre’s theorem

proof of de Moivre’s theorem

the five answers to fifth root of 1

2. Offer six (optional) chapters which "Look Back" to the important topics in algebra.

For example, the sixth of those Looking Back chapters covers:

functions

1-1, onto

domain, codomain

1-1 correspondence

the definition of the number 1

natural numbers

the definition of the number zero

whole numbers

rational numbers

irrational numbers

transcendental numbers

natural logarithms and common logarithms

e

real numbers

algebraic numbers

pure imaginary numbers

complex numbers

the complex number plane

i to the ith power is a real number (≈ 0.2078796)

3. Offers a Looking Forward to the two years of calculus and examines each of the 24 chapters in Life of Fred: Calculus Expanded Edition and describes what parts of high school math will be required for each chapter. It provides exercises for each of the topics.