Grazes
Where 0<=x<360,
Solve the equation



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Grazes
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0
\[3\sin x5+\csc x=0\]

Mertsj
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\[3\sin ^2x5\sin x+1=0\]

Grazes
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But I simplified that to \[\sin ^{2}x3\sin x+1\]

Mertsj
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I don't see how you get that?

Grazes
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Give me a sec

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

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

Mertsj
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\[3sinx \times sinx5\times sinx+\frac{1}{sinx}\times sinx=0 \times sinx\]

Mertsj
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yes

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

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

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

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

Mertsj
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so sin x = .3820

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

Mertsj
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If you have a table of values you could.

Mertsj
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Did you get 22.5 degrees and 157.5 degrees?

genius12
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Do we need my assistance here or are we ok?