anonymous 3 years ago Where 0<=x<360, Solve the equation

1. anonymous

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

2. Mertsj

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

3. anonymous

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

4. Mertsj

I don't see how you get that?

5. anonymous

Give me a sec

6. anonymous

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

7. anonymous

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. anonymous

$\frac{ 3\pm \sqrt{5}}{ 2 }$ 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. anonymous

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. anonymous

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. anonymous

Do we need my assistance here or are we ok?

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