Use what you learned in calculus to show that Sin(alpha)≤alpha and sin(alpha)/cos(alpha)≥alpha holds for all 0≤alpha≤pi/2
You can use it using geometry.
Look at the picture.
The angle between the x-axis and the red line is .
While the circle is a unit circle.
Thus, the length of the arc made by is .
While the length of the blue line is .
Now reflect that image through the x-axis (second picture).
We see that the length of the blue line is .
And the length of arc made by the blue line is .
Thus, .
This is because the shortest distance between two points is a straight line.