TABLE OF CONTENTS Euler's equation
Euler's equation also works for a positive exponent, i.e.,
When the angle in question happens to be ?,
Euler's inverse formula
if k is an integer, cos( ? + 2 ?k) = cos( ?).
From Elements of Calculus with Analytic Geometry by E. W. Swokowski [26] :
From Exploring Numerical Methods: An Introduction to Scientific Computing Using MATLAB by P. Linz and R. L. C. Wang [10] :
Cartesian to polar:
If x and y are both negative, then add ? to ?.
If x is negative but y is positive, subtract ? from ?.
If x is zero, and y is negative, then ? = ? ?/2.
If x is zero, and y is positive, then ? = ?/2.
Polar to Cartesian:
Quadratic formula:
Note: ? ? ?= ? ? ? ?, but ONLY when both ? and ? are positive integers. This is a common mistake that comes up in some DSP problems.
[26]E. W. Swokowski, Elements of Calculus with Analytic Geometry. Boston, Massachusetts: Prindle, Weber and Schmidt, 1980.
[10]P. Linz and R. L. C. Wang, Exploring Numerical Methods: An Introduction to Scientific Computing Using MATLAB. Jones and Bartlett Mathematics, 2003.
Nyquist criterion:
sampling: x( t) becomes x(
