Question

question find an angle \\( \theta \\) coterminal to \\( \frac{35\pi}{6} \\), where \\( 0 \leq \theta < 2\pi \\). answer attempt 1 out of 2

Explanation:

Step1: Identify coterminal angle rule

Coterminal angles differ by integer multiples of $2\pi$. We subtract $2\pi$ (equivalent to $\frac{12\pi}{6}$) repeatedly until the result is in $0 \leq \theta < 2\pi$.

Step2: Subtract $2\pi$ twice from $\frac{35\pi}{6}$

First subtraction: $\frac{35\pi}{6} - \frac{12\pi}{6} = \frac{23\pi}{6}$
Second subtraction: $\frac{23\pi}{6} - \frac{12\pi}{6} = \frac{11\pi}{6}$
This value is within the required interval.

Answer:

$\frac{11\pi}{6}$