# Cauchy's formula

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See Attachment for equation

We know that sin z and cos z are analytic functions of z in the whole z-plane, what can we conclude about *(see attachment for equations)* in the first quadrant

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#### Solution Preview

Find:

a) Integral [ Sin z / {z^2 - pi^2} ]

(|z| =4)

= Integral [ Sin z / {(z+pi)*(z-pi)} ]

(|z| =4)

Two poles z = -pi and z=pi both within the circle |z|=4

Therefore, Integral = 2*pi*i*{R1+R2}

where R1 and r2 are the residues ...

#### Solution Summary

This shows how to work with analytic trigonometric functions and Cacuhy's formula. The equations with new quadrants are determined.

$2.49