Download Area ratio A circular arc AB of radius 1 subtends an angle of θ

Calculus & Trigonometry
Grinshpan
Area ratio1
A circular arc AB of radius 1 subtends an angle of θ radians.
The tangent lines to the arc at points A and B meet at point C.
Express the area S(θ) of the shaded circular segment in terms of θ.
Express the area T (θ) of the triangle ABC in terms of θ.
Find the limit of the area ratio
as θ → 0.
1
Apostol, Calculus
S(θ)
T (θ)