The circumference of the unit circle is 2π so π is the length of a semicircular arc.
If the semicircle starts at (-1,0) its terminal point is (1,0).
If the semicircle starts at (0,1) its terminal point is (0,-1).
The equation of the unit circle is x2+y2=1.
The line y=ax is the equation of its diameters where a is any number. The diameter intersects the circle when:
x2+a2x2=1, x2=1/(1+a2), x=±√(1/(1+a2))
so 1/(1+a2)+y2=1, y2=1-1/(1+a2)=a2/(1+a2), y=±a/√(1+a2).
If a=1, x=y=±1/√2=±√2/2, so the arc has endpoints (√2/2,√2/2) and (-√2/2,-√2/2).
If a=-1, x=±√2/2, y=∓√2/2, endpoints are (√2/2,-√2/2) and (-√2/2,√2/2).
In general then, the endpoints are:
(√(1/(1+a2)),a/√(1+a2)) and (-√(1/(1+a2)),-a/√(1+a2)).