"Sine", if I recall correctly, is "opposite side over hypotenuse" so I might start by drawing a right triangle with leg opposite the angle equal to half the hypotenuse. Then I might realize that If I put two of those together, with the third sides as common side, I have a triangle with all three sides the same length- two sides are the two hypotenuses and the third side is made with the two 1/2 sides. What can you say about the angles in a equilateral triangle?
For the other problem, what do you know about when two angles have the same cosine? Think about the graph of y= cos(x).