using-the-unit-circle-determine-the-value-of-tan43tanfrac4pi3

Question

Using the unit circle, determine the value of $an\frac{4\pi}{3}$ .

Unit circle with coordinates and angles for trigonometric functions in trigonometry.

Accepted Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mn>3</mn></msqrt></mrow><annotation encoding="application/x-tex">\sqrt3</annotation></semantics></math>3<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg>​﻿

Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{\sqrt3}{3}</annotation></semantics></math>33<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg>​​﻿

Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">-\frac{\sqrt3}{2}</annotation></semantics></math>−23<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg>​​﻿

Answer

Undefined

Using the unit circle, determine the value of ﻿tan⁡4π3\tan\frac{4\pi}{3}tan34π​﻿.

Using the unit circle, determine the value of $\tan\frac{4\pi}{3}$ .