The Power-Amplification Formula for Sin and Cos: How to Handle Negative Inputs?

  • Thread starter Jhenrique
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For example, f(x) = √(sin(x)) = √(-1) = i. i is not a real number, so the bottom line is that there is no real function that will give the right answer for all x. Similar story for g(x) = √(cos(x)).
  • #1
Jhenrique
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Homework Statement



If exist a formula for reducion of power for sin and cos:

81f00e549acd8c0fa3f17849ed95f04b.png


a08ebbfea6efb2d1a12277214402cffb.png


So, is possible to define a formula of "amplification of power" for sin and cos?

[tex]\sqrt{\sin(x)} = ?[/tex][tex]\sqrt{\cos(x)} = ?[/tex]

Homework Equations



imagem.jpg


The Attempt at a Solution



None attempt well succeful or relevant.
 
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  • #2
Jhenrique said:

Homework Statement



If exist a formula for reducion of power for sin and cos:

81f00e549acd8c0fa3f17849ed95f04b.png


a08ebbfea6efb2d1a12277214402cffb.png


So, is possible to define a formula of "amplification of power" for sin and cos?

[tex]\sqrt{\sin(x)} = ?[/tex][tex]\sqrt{\cos(x)} = ?[/tex]

Homework Equations



imagem.jpg


The Attempt at a Solution



None attempt well succeful or relevant.

Since ##\sqrt{\sin(x)}## and ##\sqrt{\cos(x)}## do not exist (as real quantities) whenever the sin or cos are < 0, any kind of formula would need to be genuinely weird. If there were formulas at all they would need to have branch cuts in the complex plane.
 
  • #3
I didn't understand your answer.
 
  • #4
Jhenrique said:
I didn't understand your answer.
Ray is saying, suppose f(x) = √(sin(x)), where f(x) is a real function. How will it give the right answer when sin(x) is negative?
 

1. What is the power-amplification formula?

The power-amplification formula is a mathematical equation used to calculate the increase in power or energy output of a system compared to its input. It is commonly used in electrical and mechanical engineering to determine the efficiency and performance of various systems.

2. How is the power-amplification formula calculated?

The power-amplification formula is calculated by dividing the output power by the input power. It can also be expressed as the ratio of output energy to input energy. The resulting value is typically expressed as a decimal or percentage.

3. What factors affect the power-amplification formula?

The power-amplification formula is affected by various factors such as the efficiency of the system, the type of energy being amplified, and any losses or resistance within the system. Additionally, the design and components of the system can also impact the final power amplification value.

4. How is the power-amplification formula used in real-world applications?

In real-world applications, the power-amplification formula is commonly used to optimize the performance of systems such as electrical circuits, motors, and mechanical devices. It is also used in designing and testing new technologies to ensure they meet desired power output requirements.

5. Are there any limitations to the power-amplification formula?

Yes, there are limitations to the power-amplification formula. It assumes that the system is operating at a steady state and does not account for any transient effects or fluctuations. Additionally, it does not take into account external factors such as environmental conditions or external forces acting on the system.

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