## Trigonometry

### Trigonometry is a branch of mathematics that focuses on the relationships between the angles and sides of triangles

Trigonometry is a branch of mathematics that focuses on the relationships between the angles and sides of triangles. It specifically deals with the calculations and properties of the six trigonometric functions – sine, cosine, tangent, cosecant, secant, and cotangent.

Trigonometry is widely used in various fields such as physics, engineering, architecture, and navigation because of its ability to analyze the relationships between angles and distances. It plays a crucial role in solving problems involving triangles, circles, and periodic phenomena.

The trigonometric functions are defined based on the ratios of the sides of a right triangle. In a right triangle, one of the angles is 90 degrees (a right angle), and the side opposite this angle is called the hypotenuse. The other two sides are known as the adjacent and opposite sides, depending on their positions with respect to the given angle.

Here are the definitions of the six trigonometric functions:

1. Sine (sin): The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is denoted by sin(x) or sin θ.

sin(x) = opposite/hypotenuse

2. Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. It is denoted by cos(x) or cos θ.

cos(x) = adjacent/hypotenuse

3. Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite to the length of the adjacent side. It is denoted by tan(x) or tan θ.

tan(x) = opposite/adjacent

4. Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of the angle. It is denoted by csc(x) or csc θ.

csc(x) = 1/sin(x)

5. Secant (sec): The secant of an angle is the reciprocal of the cosine of the angle. It is denoted by sec(x) or sec θ.

sec(x) = 1/cos(x)

6. Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of the angle. It is denoted by cot(x) or cot θ.

cot(x) = 1/tan(x)

Trigonometry also involves concepts like radian measure, unit circle, trigonometric identities, inverse trigonometric functions, and solving trigonometric equations. Overall, it provides a powerful toolset for analyzing and solving problems related to angles, distances, and waves.

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