Trigonometric Functions and Identities

This page presents a comprehensive overview of fundamental trigonometric concepts, focusing on the basic functions and their relationships. The content is primarily centered around wartości funkcji trygonometrycznych (values of trigonometric functions) and important identities.

The page begins by listing the primary trigonometric functions: sine (sin), cosine (cos), tangent (tg), and cotangent (ctg). These functions form the basis of trigonometry and are essential for understanding more complex trigonometric relationships.

Vocabulary: Tg is an abbreviation for tangent, while ctg stands for cotangent. These are alternative notations commonly used in some mathematical texts.

A significant portion of the page is dedicated to presenting the values of trigonometric functions for specific angles, particularly 30° and 60°. This information is crucial for students learning to obliczanie wartości funkcji trygonometrycznych dla kątów od 0° do 360° (calculate trigonometric function values for angles from 0° to 360°).

Example: The value of sin 30° is given as 1/2, while cos 60° is shown as 1/2. These values are frequently used in trigonometric calculations and problem-solving.

The page also introduces important trigonometric identities. The most prominent among these is the Pythagorean identity, expressed as sin²x + cos²x = 1. This fundamental equation is often referred to as "jedynka trygonometryczna" (trigonometric unity) and serves as the basis for many other trigonometric relationships.

Definition: The Pythagorean identity (sin²x + cos²x = 1) states that for any angle x, the sum of the squares of its sine and cosine always equals 1. This is a cornerstone concept in trigonometry.

Additionally, the page touches on wzory redukcyjne (reduction formulas), which are essential for simplifying trigonometric expressions. These formulas relate trigonometric functions of complementary angles, such as sin(90°-x) and cos(90°-x), providing a method to express these functions in terms of the original angle x.

Highlight: Understanding reduction formulas is crucial for solving complex trigonometric equations and proving trigonometric identities.

The document also hints at the domain of trigonometric functions, noting x ∈ (0°, 90°), which indicates that the primary focus is on acute angles in the first quadrant of the unit circle. This range is particularly important for understanding the behavior of trigonometric functions and their values.

In conclusion, this page serves as a concise yet comprehensive reference for key trigonometric concepts, providing essential information for students and practitioners dealing with obliczanie wartości funkcji trygonometrycznych zadania (trigonometric function value calculation tasks) and related trigonometric problems.