I'm working through Rufus Isaacs's work on differential games and I need clarification on the notation used. Some context: The Value of the game is to be the minmax of the payoff which symbolically is
$$V(\mathbf{x})=\min\limits_{\phi(\mathbf{x})}\max\limits_{\psi(\mathbf{x})}\hspace{.2cm}(\text{payoff}).$$
The Lemma on Circular Vectorgrams is where I need help deciphering:
LEMMA 2.8.1. Let $u$, $v$ be any two numbers such that $$\rho=\sqrt{u^2+v^2}>0.$$ Then $$V(\mathbf{x})=\min\limits_{\phi(\mathbf{x})}\max\limits_{\psi(\mathbf{x})}\hspace{.2cm}(u\cos\phi+v\sin\phi).$$ is furnished by $\bar{\phi}$, where $$\cos\bar{\phi}=+[-]\frac{u}{\rho},\hspace{.4cm}\sin\bar{\phi}=+[-]\frac{v}{\rho}.$$ and the max[min] itself is $$+[-]\rho.$$
What does the author mean when there are these plus and minus signs by themselves?
- Rufus Isaacs, Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, Courier Corporation, 1999.