Special Trigonometric Limits

There is the limit(sinθ/θ, x=0) = 1 that is the special trigonometric limit.

Here is the proof of the limit(sinθ/θ, x=0)=1.

Area of triangle (tanθ/2) ≥ Area of sector (θ/2) ≥ Area of triangle (sinθ/2)
Multiplying each expression by 2/sinθ produces, 1/cosθ ≥ 2/sinθ ≥ 1
and taking reciprocals and reversing the inequalities yields, cosθ ≤ sinθ/θ ≤ 1
Finally, because 1 = limit(x=cosθ, x=0) ≤ limit(x=sinθ/θ, x=0) = limit(x=1, x=0) = 1
(the squeeze theorem), you can get the limit(x=sinθ/θ, x=0)=1