Question

question
find an angle \\( \theta \\) coterminal to \\( \frac{17\pi}{3} \\), where \\( 0 \leq \theta < 2\pi \\).
answer
attempt 1 out of 2

Explanation:

Step1: Identify coterminal angle rule

Coterminal angles are found by subtracting/adding $2\pi$ (full rotations).

Step2: Subtract full rotations from $\frac{17\pi}{3}$

First, convert $2\pi$ to thirds: $2\pi = \frac{6\pi}{3}$. Subtract twice (since $\frac{17\pi}{3} > 2*2\pi$):
$\frac{17\pi}{3} - 2*\frac{6\pi}{3} = \frac{17\pi}{3} - \frac{12\pi}{3}$

Step3: Calculate the result

$\frac{17\pi - 12\pi}{3} = \frac{5\pi}{3}$
Verify $0 \leq \frac{5\pi}{3} < 2\pi$ (true, as $2\pi = \frac{6\pi}{3}$).

Answer:

$\frac{5\pi}{3}$