- #1

fraggle

- 19

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**Prove Sin(x):R--->R is continuous**

## Homework Statement

Prove that Sin(x) from R to R is continous using the epsilon delta definition of continuity and the following lemma:

denote the absolute value of x by abs(x)

Lemma: abs(x)>=sin(x)

## Homework Equations

Could somebody please just tell me if my proof is correct?

The only possible problem that I see is here:

abs(sinp - sinq)=<abs[abs(p)-abs(q)]

thank you

## The Attempt at a Solution

p,q are any points in R

denote the distance between p and q by d(p,q)

for each epsilon>0 choose 0<delta<epsilon

d(p,q)=abs(p-q)<delta

d(sinq,sinq)=abs(sinp - sinq)=<abs[abs(p)-abs(q)]=<abs(p-q)<delta<epsilon