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I need help please I can only find 2 of these solutions

I need help please I can only find 2 of these solutions-example-1

1 Answer

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Step 1: Isolate the Sin Operator


8 sin((\pi )/(6) x)=2\\sin((\pi )/(6) x)=0.25\\\\

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.


x=(6 arcsin(0.25))/(\pi ) =0.48

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions


sin(x)=sin(\pi -x)

X in this case is arcsin(0.25)


(\pi )/(6) x=\pi -arcsin(0.25) = 5.52

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is


(2\pi )/(1) ((6)/(\pi ) )= 12

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

User JuCachalot
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