Option 7
Trig Functions Category 2: Sine Limit Identity

Unit 1: Limits and Continuity Option 7 Trig Functions Category 2: Sine Limit Identity

The second category of trig function limit is the Sine Limit Identity. Basically, they give you an identity for a very specific sine limit, and then you must be able to identify and use that identity.

Definition: Sine Limit Identity

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

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

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, $\lim_{x \to 0} \frac{\sin ((3 x))}{3 x} = 1$