Question

find a positive angle less than (2pi) that is coterminal with the given angle. (\frac{13pi}{3}) a positive angle less than (2pi) that is coterminal with (\frac{13pi}{3}) is (square). (simplify your answer. type your answer in terms of (pi). use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Identify coterminal angle rule

Coterminal angles differ by $2\pi k$, $k\in\mathbb{Z}$. We subtract $2\pi$ repeatedly until the result is between $0$ and $2\pi$.

Step2: Convert $2\pi$ to thirds

$2\pi = \frac{6\pi}{3}$

Step3: Subtract $2\times2\pi$ from given angle

$\frac{13\pi}{3} - 2\times\frac{6\pi}{3} = \frac{13\pi}{3} - \frac{12\pi}{3}$

Step4: Simplify the expression

$\frac{13\pi - 12\pi}{3} = \frac{\pi}{3}$

Answer:

$\frac{\pi}{3}$