matura.mkSecondary school › Trigonometry
Trigonometry: problems with solutions
113 groups of practice problems: trigonometry, from angles and the unit circle to equations and inequalities. Every problem has a step-by-step solution.
The problems are useful for the State Matura, for the external exam and for university entrance exams.
| Topic | What you practise | Problems |
|---|---|---|
| Angles and the unit circle | Quadrants, coterminal angles, degrees and radians, arcs on the unit circle. | 5 |
| Right triangles and identities | The six trigonometric ratios, special angles, simplifying expressions and proving identities. | 10 |
| Solving triangles | Law of sines, law of cosines, law of tangents and the area of a triangle. | 9 |
| Trigonometric formulas | Sum and difference, double and half angle, reduction, sum-to-product and product-to-sum formulas. | 14 |
| Trigonometric functions | Values, domain, range, signs and the order of trigonometric values. | 10 |
| Periods and graphs | Fundamental period of trigonometric functions and drawing their graphs. | 12 |
| Inverse trigonometric functions | arcsin, arccos, arctan and arccot: values, compositions, domains and equations. | 8 |
| Trigonometric equations | Basic equations, quadratic equations, factoring and sum-to-product methods. | 17 |
| Linear and homogeneous equations | a sin x + b cos x = c, homogeneous equations, maximum and minimum, parameters and systems. | 11 |
| Trigonometric inequalities | Inequalities with sin, cos, tan and cot, double inequalities, quadratic inequalities and systems. | 12 |
| Challenge problems | Range, equations with absolute value, an equation with a parameter and inverse functions. | 5 |