In this lesson, we will introduce you to the basic concepts and definitions in trigonometry, including the trigonometric functions, angles, and the unit circle.

Trigonometric Functions: Trigonometric functions are the basis of trigonometry. They are used to define the relationship between the angles and sides of a right-angled triangle. The three basic trigonometric functions are sine, cosine, and tangent, often abbreviated as sin, cos, and tan respectively.

- Sine (sin) is defined as the ratio of the length of the side opposite to an angle to the hypotenuse of a right-angled triangle. It is represented as sin(θ) = opposite/hypotenuse.
- Cosine (cos) is defined as the ratio of the length of the side adjacent to an angle to the hypotenuse of a right-angled triangle. It is represented as cos(θ) = adjacent/hypotenuse.
- Tangent (tan) is defined as the ratio of the length of the side opposite to an angle to the length of the side adjacent to the angle. It is represented as tan(θ) = opposite/adjacent.

Angles: An angle is formed by the intersection of two lines, rays, or line segments. In trigonometry, angles are measured in degrees or radians. A degree is a unit of measure of an angle, where a full rotation around a point is 360 degrees. A radian is another unit of measure of an angle, where a full rotation around a point is 2π radians.

Unit Circle: The unit circle is a circle with a radius of 1 unit. It is used in trigonometry to define the values of trigonometric functions for any angle. The unit circle is divided into 360 degrees or 2π radians. Each degree or radian on the unit circle corresponds to a specific value of the sine, cosine, and tangent functions.

Applications: Trigonometry has various applications in different fields, such as engineering, physics, astronomy, and navigation. For example, trigonometry can be used to calculate the height of a building, the distance between two points, or the position of a planet in space.

Conclusion: In conclusion, trigonometry is an essential branch of mathematics that deals with the relationships between the angles and sides of a right-angled triangle. The three basic trigonometric functions are sine, cosine, and tangent, which are defined in terms of the ratios of the sides of a right-angled triangle. Angles are measured in degrees or radians, and the unit circle is used to define the values of trigonometric functions for any angle. Trigonometry has various applications in different fields, and a solid understanding of its basic concepts and definitions is necessary for further studies in mathematics, engineering, physics, and other related fields.