Find all solutions to the equation.

7 sin^2x - 14 sin x + 2 = -5

Question

Find all solutions to the equation.

7 sin^2x - 14 sin x + 2 = -5

anonymous · Answer

I have a basic understanding for these types of problems, I am just having some difficulty with this one.

zarkon · Answer

$$7 u^2 - 14 u + 2 = -5$$

anonymous · Answer

Yes just like that

anonymous · Answer

For other problems I have factored, Im just not sure what to do with this one. Should I subtract -2 from both sides? Should I factor out the 7 from both sin terms?

zarkon · Answer

$$7 u^2 - 14 u + 7=0$$

anonymous · Answer

Okay thats what I did the first time. I then factored out 7 to be left with $$7(\sin^2x-2sinx+1)=0$$

zarkon · Answer

$$7(\sin(x)-1)^2=0$$

anonymous · Answer

That was the point where I ended. I didnt know where to take it from there.

zarkon · Answer

$$\Large\Rightarrow \sin(x)-1=0$$

anonymous · Answer

Which we would need to isolate the sin to get $$sinx=1$$

anonymous · Answer

What happens to the 7 though?

zarkon · Answer

divide both sides by 7

anonymous · Answer

so sinx=1/7? The only thing that confuses me about that, is that there is no sine or y value on the unit circle that is 1/7

zarkon · Answer

no

zarkon · Answer

$$7(\sin(x)-1)^2=0$$

$$\Rightarrow (\sin(x)-1)^2=0/7=0$$

zarkon · Answer

so you need just to find $$\sin(x)=1$$

anonymous · Answer

how does 0/7=0?

anonymous · Answer

ohhhhh

anonymous · Answer

Nevermind I get it now

zarkon · Answer

zero divided by any nonzero number is zero

anonymous · Answer

Thank you so much!

anonymous · Answer

That would be like multiplication. 0 times any number is zero.