find the exact value of tan 30°. tan 30° = (simplify your answer, including any radicals. use integers or…

Explanation:

Step1: Recall tangent formula

$\tan\theta=\frac{\sin\theta}{\cos\theta}$, so $\tan30^{\circ}=\frac{\sin30^{\circ}}{\cos30^{\circ}}$.

Step2: Know sine and cosine values

We know that $\sin30^{\circ}=\frac{1}{2}$ and $\cos30^{\circ}=\frac{\sqrt{3}}{2}$.

Step3: Calculate tangent value

$\tan30^{\circ}=\frac{\sin30^{\circ}}{\cos30^{\circ}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}$. Rationalize the denominator: $\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3}$.

Answer:

$\frac{\sqrt{3}}{3}$