Trigonometry

 Trigonometry is a branch of mathematics that deals with the study of relationships between the angles and sides of triangles. It has applications in various fields, such as physics, engineering, architecture, computer graphics, and astronomy, among others. Trigonometry is essential for understanding and solving problems related to angles, distances, and periodic phenomena.


The primary trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. These functions are defined in terms of the sides of a right-angled triangle. In a right triangle (a triangle with one angle measuring 90 degrees), the three main trigonometric ratios are:


Sine (sinθ): The ratio of the length of the side opposite the angle θ to the length of the hypotenuse (the side opposite the right angle).

sinθ = (opposite side) / (hypotenuse)


Cosine (cosθ): The ratio of the length of the adjacent side to the angle θ to the length of the hypotenuse.

cosθ = (adjacent side) / (hypotenuse)


Tangent (tanθ): The ratio of the length of the side opposite the angle θ to the length of the adjacent side.

tanθ = (opposite side) / (adjacent side)


These functions can also be defined using the unit circle, which extends their use to any angle (not just those within right triangles).


Other trigonometric functions include cosecant (cscθ), secant (secθ), and cotangent (cotθ), which are reciprocals of sine, cosine, and tangent, respectively.


Trigonometry also involves trigonometric identities, equations, and the study of trigonometric graphs, which represent the periodic nature of trigonometric functions.


Some common trigonometric identities include the Pythagorean identity, sum and difference identities, double angle identities, and half-angle identities.


Trigonometry is a fundamental topic in mathematics and plays a crucial role in various fields where angles and distances are significant. It provides valuable tools for solving a wide range of problems involving triangles and periodic functions.






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