## Grazes 2 years ago Where 0<=x<360, Solve the equation

1. Grazes

$3\sin x-5+\csc x=0$

2. Mertsj

$3\sin ^2x-5\sin x+1=0$

3. Grazes

But I simplified that to $\sin ^{2}x-3\sin x+1$

4. Mertsj

I don't see how you get that?

5. Grazes

Give me a sec

6. Grazes

Oh wait.. I was looking at something else. My bad.

7. Grazes

Would I use the quadratic formula to find the roots of 3sin^2x−5sinx+1=0?

8. Mertsj

$3sinx \times sinx-5\times sinx+\frac{1}{sinx}\times sinx=0 \times sinx$

9. Mertsj

yes

10. Grazes

$\frac{ 3\pm \sqrt{5}}{ 2 }$ But then what? I can't isolate for x, can I?

11. Mertsj

sin x = (3+sqrt5)/2 or sin x = (3-sqrt5)/2

12. Grazes

So would I find the arcsin of (3+sqrt5)/2 and (3-sqrt5)/2 for x?

13. Mertsj

Can't be the first one because sin can't be bigger than 1.

14. Mertsj

so sin x = .3820

15. Grazes

Does there happen to be a way I could solve this without using a calculator?

16. Mertsj

If you have a table of values you could.

17. Mertsj

Did you get 22.5 degrees and 157.5 degrees?

18. genius12

Do we need my assistance here or are we ok?