Trigonometry. Introduction and basic concepts

Basic concepts of trigonometry. Main trigonometric functions

The main trigonometric functions are sine, cosine and tangent. These functions are defined in terms of an acute angle within a right triangle.

Sine of an angle

The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse.

Cosine of an angle

The cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.

Tangent of an angle

The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.

Trigonometry Applications

Trigonometry has fundamental applications in various scientific, technical and practical areas:

Astronomy and navigation. It is used to calculate distances between planets, stars and determine geographic positions by measuring angles.
Engineering and architecture. It is essential in the design and construction of structures, bridges and buildings to ensure stability and accuracy in measurements.
Physics. It supports the study of wave phenomena, analysis of forces and motion, as well as optics and acoustics.
Cartography and geodesy. Helps to map and represent the earth’s surface and to measure distances and land areas.
Technology and computer graphics. It is used to model three-dimensional objects, generate graphics and visual effects in video games and animations.
Medicine and imaging. It is key in technologies such as tomography, magnetic resonance and ultrasound to interpret images of the human body.
Meteorology. Enables analysis of weather patterns and modeling of wind and storm trajectories.

Each of these applications demonstrates how trigonometry connects mathematics with the real world.