# Limit of sin x/x as x Tends to Zero

Limit of sin x/x as x Tends to Zero

Express as tanx≥x≥sinx. Divide by sinx and take reciprocals to get . Since , by the squeeze theorem, =1.

ΔOPM>sector(OPQ)>ΔOPQ

1

2

1

2

1

2

1

2

cosx≤≤1

sinx

x

cos0=1

lim

x0

sinx

x

This is the only limit needed to get the derivatives of all the trigonometric functions and their inverses.