Introduction to Basic Trigonometry

Branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides.

Trigonometry is a branch of mathematics that studies the relationships between the angles and lengths of triangles. This unit will introduce you to the fundamental concepts of Trigonometry, starting with understanding angles, the unit circle, and basic trigonometric functions.

Understanding Angles: Degrees and Radians

Angles are a measure of rotation and are fundamental to the study of Trigonometry. They can be measured in two units: degrees and radians.

• A full rotation around a circle is 360 degrees.
• In terms of radians, a full rotation is 2π radians.

The conversion between these two units is essential in Trigonometry. To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π.

The Unit Circle: Definition and Importance

The unit circle is a circle with a radius of one, centered at the origin of a coordinate plane. It's a crucial concept in Trigonometry because it provides a geometric interpretation of the sine, cosine, and tangent functions.

The x-coordinate of a point on the unit circle corresponds to the cosine of the angle formed by the positive x-axis and the line segment connecting the origin to the point. Similarly, the y-coordinate corresponds to the sine of the angle.

Basic Trigonometric Functions: Sine, Cosine, and Tangent

The three basic trigonometric functions are sine (sin), cosine (cos), and tangent (tan). They are defined as follows for a right-angled triangle:

• Sine (sin) of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
• Cosine (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
• Tangent (tan) of an angle is the ratio of the sine of the angle to the cosine of the angle, which is equivalent to the ratio of the opposite side to the adjacent side.

These functions allow us to relate the angles of a triangle to the lengths of its sides, providing the foundation for many applications of Trigonometry.

In conclusion, this unit has introduced the fundamental concepts of Trigonometry, including understanding angles, the unit circle, and basic trigonometric functions. These concepts form the basis for more advanced topics in Trigonometry, which we will explore in the following units.