# Basic Trigonometric Limit

1. Nov 12, 2008

### optics.tech

Hi everyone,

I would like to know, since the lim theta --> 0 (sine theta / theta) = 1, what is the limit theta --> 0 of cosine and tangent?

Thank you very much in advance

2. Nov 12, 2008

### Staff: Mentor

What do you think they are? The cos(theta)/theta case seems pretty easy, right? And how is the sin(theta)/theta limit calculated? Can you use the same technique in the tan(theta)/theta case?

3. Nov 12, 2008

### HallsofIvy

Staff Emeritus
What do you mean by "limit of cosine and tangent"? If you mean those functions separately, they are continuous so the limit of cosine(theta) as theta goes to 0 is cos(0)= 1. The limit of tan(theta) as theta goes to 0 is tan(0)= 0.

If you mean, as berkeman says, cos(theta)/theta, and tan(theta)/theta, all you need to know is that cos(theta)/theta has numerator close to 1 and denominator close to 0 for theta close to 0. For tan(theta)/theta, think tan(theta)= sin(theta)/cos(theta) so tan(theta)/theta= (sin(theta)/theta)/cos(theta).