Other examples:
sin(0)=cos(90°)=0; sin(90°)=cos(0); sin(45°)=cos(45°)=0.7071 (1/√2 or √2/2).
The reason comes from the word "trigonometry" which comes from "trigon" (meaning a 3-sided polygon, which is a triangle) and "metr-" (meaning measure). The "trigon" (triangle) is a right triangle so the other two angles in the triangle must add up to 90°.
sine=(opposite side length)/(hypotenuse length);
cosine=(adjacent side length)/(hypotenuse length).
What is the opposite side for sine is the adjacent side for cosine, and vice versa, hence why:
cos(x)=sin(90°-x) for angles between 0 and 90°. It's still true for angles bigger than 90° and negative angles, but it's easier to see why cosine and sine are related by looking at an "ordinary" right triangle where the relevant angles are each less than 90 degrees.