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?

`((√(3))/(2),(1)/(2))`

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

The tangent value is
`(y)/(x)`

So plug in.

`((1)/(2))/((√(3))/(2))`

`(1)/(2)*(2)/(√(3))`

The 2s will cancel out.

`(1)/(√(3))`

Rationalize by multiplying the top and bottom by
`√(3)`

`(1*√(3))/(√(3)*√(3))`

`(√(3))/(3)`

However, tangent in the fourth quadrant is negative.

`-(√(3))/(3)` is the exact value of tan(330).

Hope this helped,

chikafujiwara

よい一日を！