What is the Greek Notation in Tangent Transformations?

Click For Summary
SUMMARY

The discussion focuses on the Greek notation used in tangent transformations, specifically in the context of the equation \(Y_{tan}=A\tan\left[\omega\left(x-\frac{\phi}{\omega} \right) \right]+B\). Key variables include the period \(T\), which is defined as \(T=\left(\frac{\phi}{\omega}\right)\), and the phase shift \(PS=\phi\). An example is provided with \(Y_{49}=1+\frac{1}{2}\tan\left({2x-\frac{\pi}{4}}\right)\), where \(T=\frac{\pi}{2}\) and \(PS=\frac{\pi}{4}\). The use of Greek letters is standard in mathematical notation to represent specific parameters.

PREREQUISITES
  • Understanding of trigonometric functions, particularly tangent.
  • Familiarity with the concepts of period and phase shift in wave functions.
  • Basic knowledge of mathematical notation and transformations.
  • Ability to interpret mathematical equations and their components.
NEXT STEPS
  • Study the properties of tangent functions and their transformations.
  • Learn about the significance of phase shifts in trigonometric equations.
  • Explore the application of Greek notation in advanced mathematics.
  • Investigate the relationship between angular frequency (\(\omega\)) and period (\(T\)).
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are working with trigonometric functions and transformations, particularly those interested in wave mechanics and signal processing.

karush
Gold Member
MHB
Messages
3,240
Reaction score
5
$\textsf{got ? on the Greek notation. if Period = T}$
\begin{align}
\displaystyle
Y_{tan}&=A\tan\left[\omega\left(x-\frac{\phi}{\omega} \right) \right]+B
\implies A\tan\left(\omega x-\phi \right)+B \\
T&=\left(\frac{\phi}{\omega}\right) \\
PS&=\phi
\end{align}
$\textsf{so on:}$
\begin{align}
\displaystyle
Y_{49}&=1+\frac{1}{2}\tan\left({2x-\frac{\pi}{4}}\right) \\
T&=\frac{\pi}{2} \\
PS&=\frac{\pi}{4}
\end{align} $\textsf{not sure on this one} $
:cool:
 
Last edited:
Mathematics news on Phys.org
What is your question?
 
HallsofIvy said:
What is your question?

why is this in greek?
 

Similar threads

Replies
3
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
7K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K