It is known that the angle α is an acute angle

It is known that the angle α is an acute angle

Make the unit circle, the intersection of the unit circle and the coordinate axis at points a (1,0), B (0,1)
Let the unit circle of the final intersection of angle α be at point P and PM ⊥ X axis be made through point P,
According to the knowledge of trigonometric function line, MP = sin α, OM = cos α,
In RT △ PMO, MP + om > Op,
That is sin α + cos α > 1
Because the area of △ POA is less than that of sector POA,
So 1 / 2 &; OA &; MP