Series definitions for the sin and cosine functions are:
These converge .
If we differentiate these term by term we can see that:
Many other properties can be deduced from these power series.
The graph of is as shown:
The graph of is a reflection of (cut down) in the line .
Knowing is true, you may not deduce .
We take the positive square root because for the
Similarly we define the ‘so called’ cut down cosine – this is cosine but with the domain , and the cut down tangent with domain . The inverses of these functions are arccos and arctan.