Question

Without a calculator, evaluate tan^2(2π/3)

Answer 1

tan(-2π/-3)
= tan(2π/3)
= sin(2π/3) / cos(2π/3)
= (√3 / 2) / (-1 / 2)
= - √3

finally

tan(-2π/-3) = - √3

Answer 2

i hope it's right

Answer 3

Thanks :)

Answer 4

no problem

Answer 5

\[\tan \frac{ 2\pi }{3 }=\tan \left( \pi-\frac{ \pi }{ 3 } \right)=-\tan \frac{ \pi }{3 }=-\frac{ \frac{ \sqrt{3} }{2 } }{ \frac{ 1 }{2 }}=-\sqrt{3}\]
\[\tan ^{2}\left( \frac{ 2\pi }{3 } \right)=\left( -\sqrt{3} \right)^{2}=3\]