# Thornton & Marion, Classical Dynamics, 5th Edition

## Chapter 1. Matrices, Vectors, and Vector Calculus

### Problem 02. Trigonometric properties of direction cosines

#### Solution

For Equation (1.10): Proof)

Using Figure 1-4 (a) in the book, let the length of a point P on the line from the origin be , then

Therefore, it becomes

For Equation (1.11):

In Figure 1-4 (b) in the book, let the length of a point P on the line from the origin be and the length of a point P’ on the line be .

Using the law of cosines,

Since the equation becomes

Therefore,