evaluate without a calculator: sec 30°

Explanation:

Step1: Recall secant - cosine relationship

$\sec\theta=\frac{1}{\cos\theta}$, so $\sec30^{\circ}=\frac{1}{\cos30^{\circ}}$.

Step2: Recall value of cos 30°

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

Step3: Calculate sec 30°

$\sec30^{\circ}=\frac{1}{\cos30^{\circ}}=\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}}=\frac{2\sqrt{3}}{3}$.

Answer:

$\frac{2\sqrt{3}}{3}$