Question

use the unit circle, along with the definitions of the circular functions, to find the exact value for the function at the right, given s = 7π/3. sec 7π/3 sec 7π/3 = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Find coterminal angle

The angle $\frac{7\pi}{3}$ is coterminal with $\frac{7\pi}{3}-2\pi=\frac{7\pi - 6\pi}{3}=\frac{\pi}{3}$.

Step2: Recall secant - cosine relationship

We know that $\sec s=\frac{1}{\cos s}$. For $s = \frac{\pi}{3}$, $\cos\frac{\pi}{3}=\frac{1}{2}$.

Step3: Calculate secant value

Since $\sec\frac{\pi}{3}=\frac{1}{\cos\frac{\pi}{3}}$, substituting $\cos\frac{\pi}{3}=\frac{1}{2}$, we get $\sec\frac{\pi}{3} = 2$.

Answer:

$2$