What Are the Limits of Cosine and Tangent as Theta Approaches Zero?

[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

 

[berkeman]

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

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?

 

[HallsofIvy]

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).