Trigonometry

Definition

Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles. It provides the tools and techniques to analyze and solve problems involving angles, lengths, and the relationships between them.

5 Must Know Facts For Your Next Test

1. Trigonometry is essential for understanding and solving problems involving non-right triangles, such as those found in the Law of Sines and Law of Cosines.
2. The rotation of axes, as discussed in Topic 12.4, is a trigonometric concept that involves transforming coordinates between different coordinate systems.
3. Trigonometric functions, such as sine, cosine, and tangent, are fundamental to the study of angles and their relationships in both right and non-right triangles.
4. Trigonometry has applications in a wide range of fields, including physics, engineering, surveying, navigation, and more.
5. Mastering trigonometry requires understanding the unit circle, which provides a visual representation of the trigonometric functions and their relationships.

Review Questions

• Explain how the concept of trigonometry is applied in the context of Topic 7.1 Angles.
  • In Topic 7.1 Angles, trigonometry is essential for understanding and working with the measurement of angles. Trigonometric functions, such as sine, cosine, and tangent, are used to define the relationships between the sides and angles of triangles. These functions allow for the calculation of unknown angles or sides based on the known information, which is crucial for solving problems involving angles.
• Describe how the Law of Sines and Law of Cosines, covered in Topics 10.1 and 10.2, respectively, rely on the principles of trigonometry.
  • The Law of Sines and Law of Cosines are two key trigonometric concepts that are used to solve problems involving non-right triangles. The Law of Sines relates the sides and angles of a triangle using the sine function, while the Law of Cosines relates the sides and angles using the cosine function. These laws allow for the determination of unknown sides or angles in a triangle when at least three pieces of information are known, demonstrating the importance of trigonometry in the analysis of non-right triangles.
• Analyze how the concept of trigonometry, specifically the rotation of axes, is applied in the context of Topic 12.4 Rotation of Axes.
  • $$\text{In Topic 12.4 Rotation of Axes, trigonometry is essential for understanding and applying the rotation of coordinate systems.} \text{Trigonometric functions, such as sine and cosine, are used to define the relationships between the original and rotated coordinate axes.} \text{This allows for the transformation of coordinates between different coordinate systems, which is crucial for analyzing and solving problems involving the rotation of axes.} \text{The understanding of trigonometry and its application in this context is fundamental for mastering the concepts covered in Topic 12.4.}$$

Related terms

Angle:

A measure of the amount of rotation between two intersecting lines or planes, typically measured in degrees or radians.

Right Triangle: A triangle in which one of the angles is a 90-degree (or right) angle, and the other two angles are acute angles.

Sine, Cosine, Tangent: The three primary trigonometric functions that define the ratios between the sides of a right triangle.