5) $\\tan(-\\frac{2\\pi}{3})$ \na) $-\\sqrt{3}$ b) $-\\frac{\\sqrt{3}}{3}$ c) $\\frac{\\sqrt{3}}{3}$ d)…

5) $\\tan(-\\frac{2\\pi}{3})$ \na) $-\\sqrt{3}$ b) $-\\frac{\\sqrt{3}}{3}$ c) $\\frac{\\sqrt{3}}{3}$ d) $\\sqrt{3}$\n6) $\\tan(630^{\\circ})$

5) $\\tan(-\\frac{2\\pi}{3})$ \na) $-\\sqrt{3}$ b) $-\\frac{\\sqrt{3}}{3}$ c) $\\frac{\\sqrt{3}}{3}$ d) $\\sqrt{3}$\n6) $\\tan(630^{\\circ})$

Answer

Explanation:

Step1: Use the property of tangent function (\tan(-\alpha)=-\tan\alpha)

For (\tan(-\frac{2\pi}{3})), we have (\tan(-\frac{2\pi}{3})=-\tan\frac{2\pi}{3})

Step2: Rewrite the angle (\frac{2\pi}{3})

(\frac{2\pi}{3}=\pi - \frac{\pi}{3}), and (\tan(\pi-\theta)=-\tan\theta). So (\tan\frac{2\pi}{3}=\tan(\pi - \frac{\pi}{3})=-\tan\frac{\pi}{3})

Step3: Calculate (\tan\frac{\pi}{3})

We know that (\tan\frac{\pi}{3}=\sqrt{3})

Step4: Substitute back

(\tan(-\frac{2\pi}{3})=-(-\tan\frac{\pi}{3})=\tan\frac{\pi}{3}=\sqrt{3})

Answer:

D. (\sqrt{3})