Help Needed: Solving x and Simplifying Equations

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Discussion Overview

The discussion revolves around solving equations for a variable \( x \) and simplifying mathematical expressions. It includes requests for assistance with specific problems, as well as a word problem related to modeling current in an electrical circuit.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Participants express difficulty in solving for \( x \) and simplifying equations, seeking assistance.
  • One participant suggests changing \( \sin^2{x} \) to \( (1-\cos^2{x}) \) and solving the resulting quadratic equation for \( \cos{x} \).
  • Another participant proposes changing cosecant and cotangent to factors in terms of sine and cosine for simplification.
  • A participant reports successfully solving the initial problems and seeks help with a new word problem involving an electrical circuit.
  • In response to the word problem, another participant explains the relationship between frequency and period, providing a function for current flow as a function of time.
  • There is a mention of a horizontal shift in the sinusoidal graph due to lag in the switch.

Areas of Agreement / Disagreement

Participants generally agree on the methods proposed for solving and simplifying the equations, but the discussion remains unresolved regarding the specific application to the new word problem.

Contextual Notes

The discussion includes assumptions about the mathematical transformations and the context of the electrical circuit problem, which may not be fully explored.

bigpoppapump
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having trouble with the following, if anyone could provide assistance it would be appreciated.

Solve for x:

1619175324265.png


and

Simplify the following:
1619175453718.png
 

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bigpoppapump said:
having trouble with the following, if anyone could provide assistance it would be appreciated.

Solve for x:

View attachment 11112

and

Simplify the following:
View attachment 11113
Please show us what you have tried and exactly where you are stuck.

We can't help you if we don't where you are stuck.
 
https://mathhelpboards.com/attachments/1619175324265-png.11112/
change $\sin^2{x}$ to $(1-\cos^2{x})$ and solve the resulting quadratic equation for $\cos{x}$https://mathhelpboards.com/attachments/1619175453718-png.11113/

change the cosecant and cotangent to factors in terms of sine & cosine, then simplify
 
skeeter said:
https://mathhelpboards.com/attachments/1619175324265-png.11112/
change $\sin^2{x}$ to $(1-\cos^2{x})$ and solve the resulting quadratic equation for $\cos{x}$https://mathhelpboards.com/attachments/1619175453718-png.11113/

change the cosecant and cotangent to factors in terms of sine & cosine, then simplify
Thank you. This helps, I was stuck but I have a good idea on how to solve both of these. Will work on it tonight.
 
I have managed to solved these problems with confidence which is great. Thanks for your guidance.

I have a word problem that I’m finding it difficult to convert into an equation. Could some direction be given so I can then run with it and complete.

The question is...
An electrical circuit runs at 50Hz at 0.5amps. Due to a lag in the switch, the first maximum current is reached at 6milliseconds. Assuming no variation, find an equation to model the current in this circuit using time in milliseconds.
 
frequency is the reciprocal of period (time to complete one cycle of AC)

$T = \dfrac{1}{50} = 0.02 \text{ sec } = 20 \text{ milliseconds}$

current flow (with no lag) as a function of time in milliseconds ...

$A = 0.5 \sin\left(\dfrac{\pi}{10} \cdot t \right)$

For that period, the sinusoidal graph of current would peak at $\dfrac{T}{4} = 5 \text{ milliseconds}$

Due to the lag, there is a 1 millisecond horizontal shift in the graph ...

In future, please start a new problem with a new thread.
 
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