Trigonometry and Vector Formulas
- Reciprocal trigonometric identities
- Pythagorean identities
- Compound angle identities
- Double angle identity for tan
- Magnitude of a vector
- Scalar product
- Angle between two vectors
- Vector equation of a line
- Parametric form of the equation of a line
- Cartesian equations of a line
- Vector product
- Area of a parallelogram
- Vector equation of a plane
- Equation of a plane (using the normal vector)
- Cartesian equation of a plane
Geometry & Trigonometry: What's the Difference?
Understand how these two branches of mathematics relate and differ.
The fundamental difference lies in their focus:
- Geometry: Studies shapes, sizes, positions, and properties of space. It's concerned with figures themselves – like lines, angles, triangles, circles, and their relationships. It deals with concepts like area, volume, congruence, and similarity.
- Trigonometry: Specifically studies the relationships between the sides and angles of triangles, particularly right triangles. It uses functions (sine, cosine, tangent, etc.) to calculate unknown side lengths or angle measures based on known ones. Its focus is on the *measurements* within triangles.
Think of Geometry as describing what shapes *are*, while Trigonometry provides tools to *measure* specific aspects of triangles.
No, they are not the same, but Trigonometry is considered a part or application of Geometry. Geometry is a much broader field. Trigonometry is a specialized area that takes geometric objects (triangles) and applies algebraic principles (using functions and equations) to study their angle-side relationships numerically. You build upon geometric concepts to understand trigonometry.
Trigonometry is deeply rooted in geometry. The definitions of trigonometric functions (sine, cosine, tangent) come directly from the ratios of sides in a right triangle, a fundamental geometric shape. Many problems in geometry that involve calculating lengths or angles within triangles are solved using trigonometric methods. Trigonometry essentially provides a powerful set of tools (using angles and ratios) to tackle certain types of geometric problems that might be complex or impossible with purely geometric theorems alone.
