Understanding 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 relationships involving lengths and angles of triangles. The word "trigonometry" comes from the Greek words "trigonon" meaning triangle, and "metron" meaning measure. In this unit, we will cover the basics of trigonometry, including the definitions of sine, cosine, and tangent, and the concept of a radian.

Introduction to Trigonometry

Trigonometry is all about the inner workings of triangles. It is a study of the relationships between the sides and angles of triangles. It is particularly useful in physics, engineering, and computer science, among other fields.

Understanding Angles: Degrees and Radians

Angles are a fundamental concept in trigonometry. They can be measured in two ways: degrees and radians. A full circle is 360 degrees or 2π radians. The conversion between these two units is essential in trigonometry.

1 radian = 180/π degrees and 1 degree = π/180 radians.

Defining Sine, Cosine, and Tangent

In a right-angled triangle, the sine (sin), cosine (cos), and tangent (tan) of an angle are defined as follows:

• Sine (sin): In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.
• Cosine (cos): In a right triangle, the cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse.
• Tangent (tan): In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side.

These ratios are fundamental to understanding and calculating various aspects of triangles.

The Unit Circle

The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane. It's a crucial tool in trigonometry because it allows us to visualize the sine, cosine, and tangent of an angle.

On the unit circle, the x-coordinate of a point is 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 is the sine of that angle. The tangent of the angle is the y-coordinate divided by the x-coordinate.

By the end of this unit, you should have a solid understanding of the basics of trigonometry. These concepts will serve as the foundation for more advanced topics in trigonometry and other areas of mathematics.