How do you evaluate #tan ((2pi)/3)#? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Shell Dec 4, 2016 #tan((2pi)/3)=-sqrt3# Explanation: #tan((2pi)/3)# Recall the identity #tantheta=sintheta/costheta# According to the unit circle, #sin((2pi)/3)=sqrt3/2# and #cos((2pi)/3)=-1/2# #tan((2pi)/3) =frac{sin((2pi)/3)}{cos((2pi)/3)}=frac(sqrt3/2)(-1/2)# #=sqrt3/2 * -2/1=sqrt3/cancel2 * -cancel2/1=-sqrt3# Answer link Related questions How do you find the trigonometric functions of any angle? What is the reference angle? How do you use the ordered pairs on a unit circle to evaluate a trigonometric function of any angle? What is the reference angle for #140^\circ#? How do you find the value of #cot 300^@#? What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#? How do you know if #sin 30 = sin 150#? How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? See all questions in Trigonometric Functions of Any Angle Impact of this question 85106 views around the world You can reuse this answer Creative Commons License