Classes with mathematical text and LaTeX
Read these lessons in order. At the end of each one, a link takes you to the corresponding chapter of the interactive book, with complete demonstrations and exercises.
- Radians, arc length and trigonometric cycle
- Circular functions and periodicity
- Sine function: definition, signs and graph
- Cosine function: horizontal coordinate and graph
- Tangent function: slope, domain and graph
- Cotangent, secant and cosecant
- Fundamental relationships demonstrated
- Identities and three demonstration paths
- Reduction of the second, third and fourth quadrants
- Complements, reduction identities and parity
- Arc addition and subtraction formulas
- Sine, cosine and tangent of double and triple arc
- Division formulas and half arc tangent
- Transform sums into products and products into sums
- Fundamental equations of sine, cosine and tangent
- Intervals and classical trigonometric equations
- Arcsine, arccosine and arctangent
- Sine, cosine and tangent inequalities
- Laws of sines, cosines, projections and areas
- Heights, Heron, medians, angle bisectors and radii
- Resolution of triangles and discussion of the ambiguous case
Map of items converted to text and LaTeX
Additional readings and activities
Interactive book
The ten chapters of the interactive Trigonometry book are on this track (chapters I, V and IX also serve as a review of Fundamental II). Each one brings the theory with all the demonstrations, interactive figures and the complete list of exercises, with resolution or answer:
- II. Circular functions — exercises 23 to 72;
- III. Fundamental relationships — exercises 73 to 116;
- IV. Reduction to the 1st quadrant — exercises 117 to 125;
- VI. Transformations — exercises 131 to 192;
- VII. Equations — exercises 193 to 270;
- VIII. Inequalities — exercises 271 to 320;
- X. Any triangles — exercises 360 to 419.
After studying the chapters, take the 215 entrance exams, with immediate correction.
From reasons to functions
In high school, the ratios between the sides of a triangle expand to functions defined in the circle. Radians, coordinates, graphs, and algebraic proofs help describe spins and repeating phenomena.
Study guide
- Reread the arcs and angles, including radians and the trigonometric cycle. The notable angles connect the known triangles to exact values.
- Study circular functions, fundamental relationships and symmetries.
- Skip to transformations, equations and inequalities.
- Apply the tools to right triangles and any triangles; close with the final review.
The path presupposes familiarity with fractions, powers, roots, equations and similarity of triangles. If any of these threads are rusty, resume Fundamental II route.