Converting from sin to cos appropriately with phasors

  • #1
wellmoisturizedfrog
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1
TL;DR Summary
Difficulty understanding when to add pi/2 vs when to subtract pi/2.
My transmissions line class often features problems where the voltage is expressed as a sin, not a cos. Obviously a phase shift of pi/2 is sufficient to convert between the two. However, I have trouble understanding when adding pi/2 is appropriate as opposed to subtracting pi/2. As per my understanding, both should be sufficient to achieve the desired conversion, but my professor says otherwise. While I understand that the angle should reflect the position of the phasor in the complex domain, I still feel as though I am missing something. Could anyone offer a concrete clarification of this matter?
 
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  • #2
Can you be more specific? Note that:
$$\sin(x +\frac{\pi}2) = \cos(x)$$
 
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Likes sophiecentaur
  • #3
You might get better help if you post an actual problem, with full details, and ask that question. For any homework-type problem, you need to show as much of your own work as possible. There is a specific format for homework-type problems.
 
  • #4
wellmoisturizedfrog said:
I still feel as though I am missing something. Could anyone offer a concrete clarification of this matter?
##sin(\Theta - \frac{\pi}{2}) = -cos(\Theta)##
##sin(\Theta + \frac{\pi}{2}) = cos(\Theta)##
etc.

Can you explain a bit more about what you are unsure of?
 
  • #5
wellmoisturizedfrog said:
TL;DR Summary: Difficulty understanding when to add pi/2 vs when to subtract pi/2.

However, I have trouble understanding when adding pi/2 is appropriate as opposed to subtracting pi/2. As per my understanding, both should be sufficient to achieve the desired conversion, but my professor says otherwise.
One will convert sin() to cos(), the other will do the same, but will invert the signal, by the net phase shift of pi.
 
  • #6
wellmoisturizedfrog said:
TL;DR Summary: Difficulty understanding when to add pi/2 vs when to subtract pi/2.

but my professor says otherwise.
I wonder if he really said that or if you mis- interpreted him (i.e. just in one particular example). The 'timing of events (phases) can sometimes be very relevant but not always.
 

FAQ: Converting from sin to cos appropriately with phasors

What is a phasor?

A phasor is a complex number that represents a sinusoidal function in terms of its amplitude and phase angle. It simplifies the analysis of sinusoidal signals in electrical engineering and physics by converting differential equations into algebraic equations.

How do you convert a sine function to a cosine function using phasors?

To convert a sine function to a cosine function, you can use the phase shift relationship. A sine function can be expressed as a cosine function with a phase shift of -90 degrees (or -π/2 radians). For example, sin(ωt) can be represented as cos(ωt - π/2).

Why is it useful to convert between sine and cosine in phasor analysis?

Converting between sine and cosine is useful because it allows for consistency in representation when analyzing circuits or systems that may use either function. It also simplifies calculations involving phase differences, especially in AC circuit analysis, where voltages and currents are often expressed in phasor form.

What is the significance of the phase angle in phasor representation?

The phase angle in phasor representation indicates the shift between the voltage and current waveforms in an AC circuit. It is crucial for understanding the relationship between these quantities, determining power factor, and analyzing reactive components in the circuit.

Can you directly add or subtract sine and cosine phasors?

No, you cannot directly add or subtract sine and cosine phasors without converting them to a common form, typically either both in sine or both in cosine. You should first convert one function to the other using the appropriate phase shift before performing any addition or subtraction.

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