Answer :
330 degrees is a special angle on the unit circle.
It will be in the fourth quadrant and negative, since tangent is a negative value in the fourth quadrant.
330 degrees has a reference angle of 30 degrees, and what angle in the first quadrant has a reference angle of 30 degrees?
You probably got 30 degrees which is right.
What is the coordinates for 30 degrees?
[tex](\frac{\sqrt{3}}{2},\frac{1}{2})[/tex]
If that is what you got it is the correct answer.
The tangent value is [tex]\frac{y}{x}[/tex]
So plug in.
[tex]\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\frac{1}{2}*\frac{2}{\sqrt{3}}[/tex]
The 2s will cancel out.
[tex]\frac{1}{\sqrt{3}}[/tex]
Rationalize by multiplying the top and bottom by [tex]\sqrt{3}[/tex]
[tex]\frac{1*\sqrt{3}}{\sqrt{3}*\sqrt{3}}[/tex]
[tex]\frac{\sqrt{3}}{3}[/tex]
However, tangent in the fourth quadrant is negative.
[tex]-\frac{\sqrt{3}}{3}[/tex] is the exact value of tan(330).
Hope this helped,
chikafujiwara
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