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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

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

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
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.