Trigonometry

Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles. The word "trigonometry" comes from the Greek words "trigonon" (triangle) and "metron" (measure).

Basic Concepts

  1. Sine (sin), Cosine (cos), and Tangent (tan): These are the basic functions of trigonometry, which are ratios of the lengths of sides in a right triangle. For an angle θ in a right triangle:

    • sin(θ) = Opposite Side / Hypotenuse
    • cos(θ) = Adjacent Side / Hypotenuse
    • tan(θ) = Opposite Side / Adjacent Side

  2. Cosecant (csc), Secant (sec), and Cotangent (cot): These are the reciprocals of sine, cosine, and tangent, respectively.

  3. Radians: This is a unit of angle measurement. A full circle is 2π radians.

  4. Unit Circle: A circle with a radius of 1, centered at the origin of a coordinate plane. The unit circle is often used in trigonometry to define trigonometric functions.

  5. Trigonometric Identities: These are equations that are true for all values of the variables. The Pythagorean trigonometric identity is an example: [sin(θ)]² + [cos(θ)]² = 1.

Applications

Trigonometry has a wide range of applications in various fields of science and engineering, including physics, computer graphics, signal processing, acoustics, electronics, celestial mechanics, and more. It's also fundamental in calculus and other advanced areas of mathematics.