Question

Where 0<=x<360,
Solve the equation

Answer 1

\[3\sin x-5+\csc x=0\]

Answer 2

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

Answer 3

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

Answer 4

I don't see how you get that?

Answer 5

Give me a sec

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

yes

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

so sin x = .3820

Answer 15

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

Answer 16

If you have a table of values you could.

Answer 17

Did you get 22.5 degrees and 157.5 degrees?

Answer 18

Do we need my assistance here or are we ok?