The value of α\alphaα is in the fourth quadrant, where cosine is negative. Since cos(π6)=32\cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2}cos(6π)=23, we have cos(α)=−cos(2π3)=−32\cos(\alpha)=-\cos(\frac{2\pi}{3})=-\frac{\sqrt{3}}{2}cos(α)=−cos(32π)=−23. Therefore, α=−2π3\alpha = -\frac{2\pi}{3}α=−32π.
The value of α\alphaα is in the fourth quadrant, where cosine is negative. Since cos(π6)=32\cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2}cos(6π )=23 , we have cos(α)=−cos(2π3)=−32\cos(\alpha)=-\cos(\frac{2\pi}{3})=-\frac{\sqrt{3}}{2}cos(α)=−cos(32π )=−23 . Therefore, α=−2π3\alpha = -\frac{2\pi}{3}α=−32π .