Finding the "Larger" of Two Cosine Values

Question

The question is as follows:

Without using a calculator, choose the larger of $\cos 310^\circ$ and $\cos 311^\circ$. Explain.

I am having difficulty understand the meaning of the word "larger" in this context. Does it possibly mean a value that is $\cos310^\circ < \cos\theta < \cos311^\circ$? If so, then would be a possible number be $\cos310.5^\circ$? Any help will be greatly appreciated!

Answer 1

HINT

Note that in the fourth quadrant, that is for $270°\le \theta \le360°$, $\cos \theta$ is increasing up to 1.

Answer 2

Using Prosthaphaeresis Formulas,

$$\cos310-\cos311=2\sin(0.5)\sin(300.5)$$

Now $$\sin(300.5)=\sin(360-59.5)=-\sin59.5<0$$