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]
