MHB Help Needed: Solving x and Simplifying Equations

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The discussion revolves around solving for x and simplifying equations, with participants providing guidance on mathematical techniques. Key suggestions include converting trigonometric functions into sine and cosine terms and solving quadratic equations. A user successfully applies the advice and gains confidence in solving the initial problems. Additionally, a word problem regarding an electrical circuit is presented, where the correct equation for modeling current is derived using sinusoidal functions. The conversation emphasizes the importance of clarity in presenting problems for effective assistance.
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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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