Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 59

Equation of a tangent line to the graph of function f at point (x_0,y_0) is given by y=y_0+f'(x_0)(x-x_0).
The first step to finding equation of tangent line is to calculate the derivative of the given function.
y'=2cdot1/sqrt(1-x^2)
Now we calculate the value of the derivative at the given point.
y'(1/2)=2/sqrt(1-(1/2)^2)=2/sqrt(1-1/4)=2/sqrt(3/4)=2/(sqrt3/2)=4/sqrt3=(4sqrt3)/3
We now have everything needed to write the equation of the tangent line.
y=pi/3+(4sqrt3)/3(x-1/2)
y=(4sqrt3)/3x+(pi-2sqrt3)/3
Graph of the function along with the tangent line can be seen in the image below.