Question

find a positive angle less than 2π that is coterminal with the given angle.
\\(\frac{38π}{5}\\)

a positive angle less than 2π that is coterminal with \\(\frac{38π}{5}\\) is \\(\square\\).
(simplify your answer. type your answer in terms of π. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Find number of full rotations

Full rotation = $2\pi = \frac{10\pi}{5}$. Divide $\frac{38\pi}{5}$ by $\frac{10\pi}{5}$: $38 \div 10 = 3$ full rotations (remainder 8).

Step2: Calculate coterminal angle

Subtract $3 \times 2\pi = 6\pi = \frac{30\pi}{5}$ from $\frac{38\pi}{5}$: $\frac{38\pi}{5} - \frac{30\pi}{5} = \frac{8\pi}{5}$.

Answer:

$\frac{8\pi}{5}$