The title is misleading - you do not need to use a cosine curve. You need to look at the unit circle instead.

Here is a diagram, which shows you an example of how to use it. Say, you're looking for other answers for cos 30. The other answers would be the ones shown in the diagram, but for the "Sine" and "Tan" quadrant, it will be negative, for the "Cos" quadrant it will be positive. So:

cos 30 = -cos 150 = cos 210 = -cos 330.

Now, refering to your questions:

Cos 20 = -cos 170. You can check it up on a calculator to check.

Cos 85 = -cos 175.

I hope you understand the above stuff, I wasn't too clear!