Asked by Anonymous
what is the inverse tangent of negative root3/3
Answers
Answered by
Reiny
let tan^-1 (-√3/3) = Ø
then tanØ = -√3/3
I know tan 30° or tan π/6 = +√3/3
Ø must be in quadrants II or IV
in degrees: Ø = 180-30=150° or Ø = 360-30 = 330°
in radians: Ø = π - π/6 = 5π/6 or Ø = 2π-π/6 = 11π/6
notice that your calculator gives you -30° or -π/6
which is correct since -30° is coterminal with 330°
calculators have been programmed to give the closest answer to zero, which in this case is -30°
the smallest positive answer is 5π/6
then tanØ = -√3/3
I know tan 30° or tan π/6 = +√3/3
Ø must be in quadrants II or IV
in degrees: Ø = 180-30=150° or Ø = 360-30 = 330°
in radians: Ø = π - π/6 = 5π/6 or Ø = 2π-π/6 = 11π/6
notice that your calculator gives you -30° or -π/6
which is correct since -30° is coterminal with 330°
calculators have been programmed to give the closest answer to zero, which in this case is -30°
the smallest positive answer is 5π/6
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