Question

Which of the following is the correct ratio for tan(2π3) ?(1 point) Responses tan(2π3)=−3√212=−3–√ tangent left parenthesis Start Fraction 2 pi over 3 End Fraction right parenthesis equals Start Fraction negative Start Fraction Start Root 3 End Root over 2 End Fraction over Start Fraction 1 over 2 End Fraction End Fraction equals negative Start Root 3 End Root tan(2π3)=−3√2−12=3–√ tangent left parenthesis Start Fraction 2 pi over 3 End Fraction right parenthesis equals negative Start Fraction Start Fraction Start Root 3 End Root over 2 End Fraction over negative Start Fraction 1 over 2 End Fraction End Fraction equals Start Root 3 End Root tan(2π3)=3√2−12=−3–√ tangent left parenthesis Start Fraction 2 pi over 3 End Fraction right parenthesis equals Start Fraction Start Fraction Start Root 3 End Root over 2 End Fraction over negative Start Fraction 1 over 2 End Fraction End Fraction equals negative Start Root 3 End Root tan(2π3)=−123√2=−3√3

Answer 1

The correct ratio for tan(2π/3) is tan(2π/3) = -√3.

Answer 2

360/3 = `120 degrees
That is quadrant 2. left upper, 60 degrees above the -x axis
y / x = -tan 60 = - sin 60 / cos 60 = -(sqrt 3 / 2 ) / (1/2) = -sqrt 3 indeed

Answer 3

I apologize for the confusion. You are correct. The correct ratio for tan(2π/3) is indeed -√3.