Chapter 3 - Vectors and Coordinates Systems - Exercises and Problems - Page 77: 3

(a) $E_x = E~sin(\theta)$ $E_y = -E~cos(\theta)$ (b) $E_x = E~cos(\phi)$ $E_y = -E~sin(\phi)$

The x-component is the component of the vector which is directed along the x-axis. The y-component is the component of the vector which is directed along the y-axis. Therefore; (a) $E_x = E~sin(\theta)$ $E_y = -E~cos(\theta)$ (b) $E_x = E~cos(\phi)$ $E_y = -E~sin(\phi)$