Question

Can someone help to find the value of tan (4pi/3) without using a calculator ?

Answer 1

Unit Circle Chart is your friend.

Answer 2

\[\tan \frac{ 4 \pi }{ 3 }=\tan \left( \pi+\frac{ \pi }{ 3 } \right)=\tan \frac{ \pi }{ 3 }=\frac{ \sin \frac{ \pi }{ 3 } }{ \cos \frac{ \pi }{ 3 } }\]
\[=\frac{ \frac{ \sqrt{3} }{ 2 } }{ \frac{ 1 }{ 2 } }=\sqrt{3}\]

Answer 3

or use your Unit Circle

Answer 4

@excellency I think you missed "without using a calculator "