Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It involves the study of trigonometric functions such as sine, cosine, and tangent, which are used to calculate unknown angles or side lengths in a triangle. The [[Pythagorean theorem]] is a fundamental theorem in trigonometry that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Trigonometry and the Pythagorean theorem are closely connected because trigonometric functions are defined based on ratios between different sides of a triangle. For example, in a right triangle, if we know one angle and one side length (other than the hypotenuse), we can use trigonometric functions to find other unknown side lengths or angles. The most commonly used trigonometric functions are sine, cosine, and tangent. Sine (sin) represents the ratio between the length of the side opposite an angle and the hypotenuse. Cosine (cos) represents the ratio between the length of an adjacent side and hypotenuse. Tangent (tan) represents the ratio between the length of an opposite side and an adjacent side. These trigonometric functions can be used together with Pythagorean theorem to solve various problems involving triangles. By using these functions and applying Pythagorean theorem appropriately, we can find missing angles or side lengths in both right triangles and non-right triangles. In summary, trigonometry helps us understand and calculate relationships between angles and sides in triangles using trigonometric functions. The Pythagorean theorem is an essential concept within trigonometry as it connects to finding unknowns in right triangles by relating their sides' lengths. # References ```dataview Table title as Title, authors as Authors where contains(subject, "trigonometry") or contains(title, "trigonometry") or contains(subject, "Trigonometry") or contains(title, "Trigonometry") ```