kvadránszögben

A kvadránszögben, also known as a quadrant angle in English, refers to an angle whose terminal side lies on one of the coordinate axes in a Cartesian coordinate system. These angles are specifically 0 degrees, 90 degrees, 180 degrees, 270 degrees, and 360 degrees (which is coterminal with 0 degrees). In radians, these angles correspond to 0, pi/2, pi, 3pi/2, and 2pi.

The term "quadrant angle" is used because the terminal side of these angles falls on the boundary between quadrants rather than within a quadrant. For instance, an angle of 90 degrees has its terminal side along the positive y-axis, separating the first and second quadrants. Similarly, an angle of 180 degrees lies on the negative x-axis, between the second and third quadrants.

Trigonometric functions evaluated at quadrant angles have specific and often simple values. For example, the sine of 0, pi/2, pi, 3pi/2, and 2pi are 0, 1, 0, -1, and 0 respectively. The cosine values are 1, 0, -1, 0, and 1. Tangent, cotangent, secant, and cosecant also have defined or undefined values at these angles, depending on the specific function and angle. Understanding quadrant angles is fundamental in trigonometry for simplifying calculations and analyzing periodic behavior of trigonometric functions. They serve as reference points for understanding angles in all parts of the coordinate plane.