Question

which angle is coterminal with \\( \frac { 7 pi } { 4 } \\)?
\\( \frac { 11 pi } { 4 } \\)
\\( \frac { pi } { 4 } \\)
\\( - \frac { 9 pi } { 4 } \\)

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are given by \(\theta + 2k\pi\), where \(k\in\mathbb{Z}\).

Step2: Check each option

• For \(\frac{11\pi}{4}\): \(\frac{7\pi}{4}+2\pi=\frac{7\pi + 8\pi}{4}=\frac{15\pi}{4}

eq\frac{11\pi}{4}\)

• For \(\frac{\pi}{4}\): \(\frac{7\pi}{4}- 2\pi=\frac{7\pi-8\pi}{4}=-\frac{\pi}{4}

eq\frac{\pi}{4}\)

• For \(-\frac{9\pi}{4}\): \(\frac{7\pi}{4}-4\pi=\frac{7\pi - 16\pi}{4}=-\frac{9\pi}{4}\)

Answer:

\(-\frac{9\pi}{4}\)