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Solve for x

bigpoppapump

New member
Apr 23, 2021
7
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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jonah

Member
Feb 21, 2015
94

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
871

change $\sin^2{x}$ to $(1-\cos^2{x})$ and solve the resulting quadratic equation for $\cos{x}$




change the cosecant and cotangent to factors in terms of sine & cosine, then simplify
 

bigpoppapump

New member
Apr 23, 2021
7


change $\sin^2{x}$ to $(1-\cos^2{x})$ and solve the resulting quadratic equation for $\cos{x}$




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.
 

bigpoppapump

New member
Apr 23, 2021
7
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.
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
871
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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