Trigonometry (11th Edition) Clone

The positive square root should be selected. $$\cos58^\circ=\sqrt{\frac{1+\cos116^\circ}{2}}$$
$$\cos58^\circ=\pm\sqrt{\frac{1+\cos116^\circ}{2}}$$ Whether the positive or negative square root should be selected depends the sign of $\cos58^\circ$. $58^\circ$ lies in quadrant I. In quadrant I, $\cos\theta\gt0$. Therefore, $\cos58^\circ\gt0$. Thus, the positive square root should be selected. In other words, $$\cos58^\circ=\sqrt{\frac{1+\cos116^\circ}{2}}$$