Question

what is the reference angle for \\(\frac{5\pi}{3}\\)\
\\(\frac{\pi}{6}\\)\
\\(\frac{\pi}{3}\\)\
\\(\frac{2\pi}{3}\\)\
complete\
what is \\(\sec\left(\frac{5\pi}{3}\
ight)\\)?\
done\
image of unit circle with angles marked

Explanation:

Step1: Find reference angle for $\frac{5\pi}{3}$

$\frac{5\pi}{3}$ is in Quadrant IV. Reference angle = $2\pi - \frac{5\pi}{3} = \frac{\pi}{3}$.

Step2: Calculate $\sec(\frac{\pi}{3})$

$\sec(\theta) = \frac{1}{\cos(\theta)}$. $\cos(\frac{\pi}{3}) = \frac{1}{2}$, so $\sec(\frac{\pi}{3}) = 2$.

Step3: Determine sign of $\sec(\frac{5\pi}{3})$

Cosine is positive in Quadrant IV, so secant is positive.

Answer:

2