The right angle on the cover of mathematics textbooks is usually used to express geometric concepts and relationships in mathematics. A right angle is a special angle, which means that the angle formed by two intersecting line segments is 90 degrees. In geometry, right angle is a very important concept, which is closely related to many other concepts and properties.

First of all, right angles are the basis of orthogonal relations. In plane geometry, two perpendicular lines are called orthogonal lines. The characteristic of orthogonal lines is that the angles they form are right angles. Right angles are often used in architecture, design, engineering and other fields because the orthogonal relationship is stable and reliable.

Secondly, right angles are the characteristic properties of rectangles and squares. A rectangle is a quadrilateral with four right angles, while a square is a special rectangle with four equal sides and four right angles. Rectangular and square have many important properties and applications in geometry, such as calculating perimeter, area and so on.

In addition to the concept related to shape, right angles are also related to trigonometric functions. In trigonometry, right angle is an important special angle in trigonometric function. For example, sine function and cosine function take maximum and minimum values at 90 degrees. The tangent function is undefined at 90 degrees. These trigonometric functions are widely used in physics, engineering, computer graphics and other fields.

In addition, the right angle is the basis of Pythagorean theorem. Pythagorean theorem refers to the mathematical relationship that the square of the hypotenuse in a right triangle is equal to the sum of the squares of two right-angled sides. This theorem plays an important role in solving geometric problems and measuring distances.

Finally, right angles are also related to coordinate systems and vectors. In rectangular coordinate system, right angles are used to represent the vertical relationship between coordinate axes. The number and direction of vectors can be expressed by vectors in rectangular coordinate system. Cartesian coordinate system and vector play an important role in geometry, physics and engineering.

To sum up, the right angle on the cover of mathematics textbooks represents many important concepts and relationships in mathematics, such as orthogonal relation, rectangle and square, trigonometric function, pythagorean theorem, rectangular coordinate system, vector and so on. As a basic concept, right angle runs through all branches of mathematics and plays an important role in real life and application.