Trigonometry in the Complex Plane

It is also possible to define cofunctions in analogy with Eq. (4.10), namely the cotangent and cosecant  

This completes the list of standard trigonometric functions. In terms of sine and cosine  

In Fig, 3.4, a complex quantity z was represented by its Cartesian coordinates X and y. Alternatively, a point in the x, y plane can be represented in polar coordinates, usually designated r and 0. Conventionally, r is the distance from the origin, while 0 is the angle that the vector r makes with the positive x axis. The coordinates in the two systems are related by 

A complex quantity z = x + iy expressed in polar coordinates is called a phasor. In place of r, we have the modulus z. The angle 0, now called the 

A convenient abbreviation that we will use for a short while is 

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