Trigonometry

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Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles.It has applications in various fields, including physics, engineering, astronomy, architecture, computer graphics, and more.

The three primary trigonometric functions are sine, cosine, and tangent, often abbreviated as sin, cos, and tan, respectively.

These functions are defined in terms of the ratios of the sides of a right-angled triangle.

In a right triangle, which is a triangle with one angle measuring 90 degrees, the three sides are typically referred to as follows:

1. Hypotenuse (H): The side opposite the right angle (the longest side).
2. Opposite side (O): The side opposite the angle you are interested in.
3. Adjacent side (A): The side adjacent to the angle you are interested in (i.e., connected to the angle).

The primary trigonometric functions are defined as follows:

1. Sine (sin θ) = O/H
2. Cosine (cos θ) = A/H
3. Tangent (tan θ) = O/A

In addition to these three functions, there are three reciprocal trigonometric functions:

4. Cosecant (csc θ) = 1/sin θ
5. Secant (sec θ) = 1/cos θ
6. Cotangent (cot θ) = 1/tan θ

Trigonometry is not only about right triangles; it also extends to deal with any kind of triangle and various other aspects of angles and periodic functions.

Some key trigonometric identities and formulas include the Pythagorean identities, sum and difference formulas, double angle formulas, half-angle formulas, and more.

Here are the Pythagorean identities, which hold for any angle θ:

• sin^2 θ + cos^2 θ = 1
• 1 + tan^2 θ = sec^2 θ
• 1 + cot^2 θ = csc^2 θ

Trigonometry is a fundamental topic in mathematics and forms the basis for many other mathematical concepts.

It helps in solving problems related to distances, heights, angles, and oscillations, among many other applications.

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