Geometric point of view
In school, one usually learns about trigonometry from triangles and circles. Just to recall, if one has a right angled triangle $\Delta PDO$ (with the right angle at $D$), then the sine and cosine of $\angle POD = \theta$ is given by
\[\sin\theta = \frac{PD}{OP}, \qquad \cos\theta = \frac{OD}{OP}.\]These are the fundamental trigonometric definitions from which everything else in the subject can be derived. However, this definition can only work for angles which are less than $90^\circ$ - we can consider them to be functions mapping $(0, 90^\circ)$ to $\mathbb{R}$ - so what do we do for more general triangles, or in mathematical terms, how do we extend the domain of definition for other angles?
About the author
Rohan Didmishe is a student of IISER Kolkata. This particular article placed fourth in our Article Writing Contest, 2022.