Question

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

Answer 1

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