This is a good one.
Let's look at O and P as points on a triangle, and we'll draw a line straight down from P and call it N. We know that the distance from O to N is sqrt of 3 and that P to N is 1. The angle at N is 90 since we drew the line straight down from P. So we now know that we have a right angle triangle that has two sides coming of the right angle with lengths of sqrt3 and 1. With this we can figure out the distance from O to P as (sqrt3)^2 + 1^2 = 4, so the radius is sqrt4, or 2.
This looks a lot like the lengths of a right angle triangle that give us the 30-60-90 triangle. Since length N-P is 1, angle PON must be 30. Now we have 2 angles that make out the 180 degrees of the X axis, 30 and 90 (as shown by the original triangle OPQ). That means that if we were to draw a line straight down from Q to a point S on the x axis we'd have a triangle where angle QOS=60.
Confused yet? I think I am. Anyway.
Looking at triangle QOS we know that angle QOS is 60 degrees, and angle OSQ is 90, so angle SQO must be 30 degrees. We also know the radius to be 2, so side OQ is 2. That means, based on our 30-60-90 triangle that OS=1 and SQ=sqrt3. Since what we're looking for is the value of "s", the length of OS is sufficient, s=1.
The diagram makes it look like the right angle triangle is equal on both sides of the y axis, but if that were the case, the values for the x and y coordinates on the circle would be the same. This would likely be a lot easier to explain if I could draw it for you.
