What is the exact value of $tan -330$ ?

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Answer 1 · 2015-05-10T09:02:15

Assuming you mean degrees, $tan(-330) = tan(30) = 1/sqrt(3) = sqrt(3)/3$ .

$sin(30) = 1/2$ , $cos(30) = sqrt(3)/2$ and $tan(30) = sin(30) / cos(30)$ .

To see this for yourself, consider an equilateral triangle with sides of length 1, then cut it in half to produce 2 right angled triangles.

These smaller triangles will have internal angles of $30$ , $60$ and $90$ degrees.

The shortest side is of length $1/2$ , so

$sin(30) = (1/2)/1 = 1/2$ .

The hypotenuse is of length 1, so the other side will have length
$sqrt(1^2 - (1/2)^2)$ = $sqrt(3/4)$ = $sqrt(3)/2$ .

What is the exact value of tan -330tan -330?