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Limit of sin(x) = x (as x tends towards 0)

Consider this diagram. There are three shapes drawn about the unit circle and the angle POA = x 1. Area of Triangle OBA = base x height - now base = 1 and tan(x) = since OA = 1 height = tan(x) Area = tan(x) 2. Area of Triangle OPA = ab sinC - now a and b = 1 (since it is the unit circle) Area = sin(x) 3. Area of the sector = the fraction of the circle x the area of the circle.. And since r =1 Area =
The area of the sector is obviously between the areas of the triangles. Therefore We can multiply everything by 2 Now tan (x) is sin (x) divided by cos (x) Now as x tends towards zero. cos(x) tends towards 1. So we get Therefore using this squeeze principle as x tends toward zero sin(x) = x