Defining Trigonometry
Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles, particularly right-angled triangles. It uses specific functions to relate angle measures to ratios of side lengths, enabling the calculation of unknown angles or side lengths within a triangle.
Core Trigonometric Functions
The fundamental trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions define ratios of the sides of a right triangle relative to a given acute angle: sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent.
Practical Application: Calculating Height
Imagine needing to find the height of a flagpole. By standing a known distance from its base and measuring the angle of elevation to its top, you can use the tangent function (tan(angle) = opposite/adjacent) to calculate the flagpole's height without physically climbing it.
Importance Across Disciplines
Trigonometry is vital in numerous fields, including engineering, physics, architecture, navigation, surveying, and computer graphics. It helps design structures, model wave phenomena, plot courses, and create realistic 3D environments, making it a cornerstone of applied mathematics.