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#.