Question

what is tan (-2pi/3)
what is sin (-7pi/3)

Answer 1

\[\tan \left( \frac{ -2\pi }{3 } \right)=-\tan \frac{ 2\pi }{3 }=-\tan \left( \pi-\frac{ \pi }{ 3 } \right)\]
\[=-\left( -\tan \frac{ \pi }{3 } \right)=\tan \frac{ \pi }{3 }=\frac{ \sin \frac{ \pi }{ 3 } }{ \cos \frac{\pi }{ 3 } }\]
\[=\frac{ \frac{ \sqrt{3} }{2 } }{\frac{ 1 }{2 } }=\frac{ \sqrt{3} }{2 }*\frac{ 2 }{1 }=\sqrt{3}\]
similarly sin (-7 pi/3) can be calculated.

Answer 2

so, would sin (-7pi/3) be (-pi/3)