Please just explain/show how to set up #1. I want to do the work on my own
and please someone check my work on 2 and 3
please hurry this is due in an hour and a half

Answer:

See below.

Step-by-step explanation:

We have:

[tex]\frac{\sqrt3}{\sin(\theta)}=2[/tex]

And we want to find two different angles between 0 and 180 that satisfy this equation.

First, let's get our sine out of the denominator. Notice that this is the same as:

[tex]\frac{\sqrt3}{\sin(\theta)}=\frac{2}{1}[/tex]

Cross-multiply:

[tex]2\sin(\theta)=\sqrt{3}[/tex]

Divide both sides by 2:

[tex]\sin(\theta)=\frac{\sqrt{3}}{2}[/tex]

Here you go! I'll have the answer for you if you scroll down, so check it when you're ready!

#2 is correct. However, double check #3. The answer's down there too... :)

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Answer for 1)

We have:

[tex]\sin(\theta)=\sqrt{3}/2[/tex]

So, at what points between 0 and 180 does sine equal √3/2?

If we refer to the unit circle, we can see that this happens twice: at 60.

Thus, the second time it occurs will be at 180-60 or 120.

So:

[tex]\theta=60\textdegree\text{ or } 120\textdegree[/tex]

Answer for 3)

So you are correct for the first three. So:

[tex]\sin(54)=t[/tex]

However, sine stays positive. So, our angle must be between 0 and 180.

So, instead of 180+54, it should be 180-54, giving us:

[tex]\sin(54)=\sin(126)=t[/tex]

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