Question

What is tan 330 degrees

Answer 1

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?

$(\frac{\sqrt{3}}{2},\frac{1}{2})$

If that is what you got it is the correct answer.

The tangent value is $\frac{y}{x}$

So plug in.

$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

$\frac{1}{2}*\frac{2}{\sqrt{3}}$

The 2s will cancel out.

$\frac{1}{\sqrt{3}}$

Rationalize by multiplying the top and bottom by $\sqrt{3}$

$\frac{1*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$\frac{\sqrt{3}}{3}$

However, tangent in the fourth quadrant is negative.

$-\frac{\sqrt{3}}{3}$ is the exact value of tan(330).

Hope this helped,

chikafujiwara

よい一日を！