Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

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