which of the following is the correct ratio for tan(7π/6)? (1 point) o tan(7π/6) = (√2/2)/(-1/2) = √3 o…

Explanation:

Step1: Rewrite the angle

We know that $\frac{7\pi}{6}=\pi+\frac{\pi}{6}$. The tangent - function has the property $\tan(A + \pi)=\tan(A)$. So, $\tan(\frac{7\pi}{6})=\tan(\pi+\frac{\pi}{6})=\tan(\frac{\pi}{6})$.

Step2: Recall the values of sine and cosine for $\frac{\pi}{6}$

For $\theta=\frac{\pi}{6}$, $\sin(\frac{\pi}{6})=\frac{1}{2}$ and $\cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2}$.

Step3: Use the tangent formula

The formula for tangent is $\tan\theta=\frac{\sin\theta}{\cos\theta}$. Substituting $\theta = \frac{\pi}{6}$, we get $\tan(\frac{\pi}{6})=\frac{\sin(\frac{\pi}{6})}{\cos(\frac{\pi}{6})}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$.

Answer:

$\tan(\frac{7\pi}{6})=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{\sqrt{3}}{3}$, so the correct option is the one with $\tan(\frac{7\pi}{6})=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{\sqrt{3}}{3}$ (the last option in the list you provided).