How to take Inverse functions out of an answer?

[SGT_Chubbz]

I thought I had the problem done right, but I didn't see the part of the question that said to eliminate inverse functions in the answer...

here's the exact text:
"Solve each of the following for x in radians. When possible, eliminate inverse trig functions in your answers."
a.) Sin(5x)= -1/3

So what I did (before i saw the eliminate inverse functions in the answer part...):

Sin is Negative in the 3rd and 4td quadrants, so,

(for simpler typing, K is any integer, since i can't type that strange 'Z' type symbol...)

5x=2K(pi)-arcsin(1/3) Or 5x = 2K(pi)+(pi)+arcsin(1/3)

those both simplify down into:

x = 1/5(2K(pi)-arcsin(1/3)) Or x = 1/5(2K(pi)+pi+arcsin(1/3))

Can anyone advise me on what to do to eliminate the inverse functions from my answers? (I have another problem just like this one but it's for tan(2x+3)=4, would that be changed the same way?)

Thank you!!

 

[HallsofIvy]

You can't take the inverse functions out of the solution- they are necessary. Why would you want to? The instructions said "when possible". If you had, for example, \(\displaystyle sin^{-1}(\sqrt{2}/2)\) then you could replace it with \(\displaystyle \pi/4\).