Began with a recap of the definition of a limit of a function. Then stated and used a proposition which listed basic properties of limits. These properties are useful for making calculations.
The second half of the lecture was devoted to definitions and basic properties of the sine, cosine and tangent functions.
For more details and illustrative examples on the basic properties of limits read Section 2.3 in Stewart.
For more details on sines, cosines and tangents read Section 1.2 in Stewart.