Using trigonometry for path finding and resource search

Hi there,

Please imagine this situation. You have landed on some random flat

planet (Cartesian coordinate plane), I would like to learn how to

properly use trigonometry to help me navigate this planet, in

search for "resources", but am not really sure how to apply trig to

this.

The constraints and rules for the scenario:

you can move in any direction (the planet wraps around itself). So if

I landed at point ---5, 5 and wanted to move to -3 -5, I would apply

the offset 2,-10.

Stopping to scan the area for the resources, your sight is limited to

some range. The sight range(radar) is effectively the radius given by

2 * your Sight Distance.

Assuming I know the height and width of the planet, and have a sight

distance of 4, what would be the best use and approach to devising the best path for covering the entire map in search of resources.

P.S I can't unfortunately have an infinite sight distance, I have 9

points to distribute between speed, power and sight range. Where you

start on planet is totally random.

...

Well I understand basic trigonometry, but I just can't visualize how

can apply it properly in this situation.

...

I must say I have struggled with figuring something out(Worried), I have tried to sketch out some movements but just need up with a bunch of seemingly

random triangles, with what appears in the middle to be the commutative

sight radius covered by the movements that created the triangles -- nothing really useful (Headbang).

Any help would be appreciated, thanks!