Option 8
Trig Functions Category 3: Cosine Limit Identity

Unit 1: Limits and Continuity Option 8 Trig Functions Category 3: Cosine Limit Identity

The third category of trig function limits is another very specific identity that involves cosine. This identity is not used nearly as often as the Sine Limit Identity. It is one of those identities that you could probably get by without knowing, but if you want to make sure you are ready for everything, you might want to commit it to memory.

Definition: Cosine Limit Identity

$\lim_{x \to 0} \frac{1 - \cos ((x))}{x} = 0$

$\lim_{x \to 0} \frac{x}{1 - \cos ((x))} = 0$

Note:

– The limit identity only applies for $x \to 0$ .

– The limit identity works the same no matter which format you have for the original limit.

– The limit has the same value as long as whatever is inside the sine function, $x$ , matches exactly with the piece on the other side of the fraction, $x$ .

For example, $\lim_{x \to 0} \frac{1 - \cos ((3 x))}{3 x} = 0$