Question

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

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are given by $\theta\pm2k\pi$, where $k$ is an integer.

Step2: Check each option

• For $\frac{\pi}{4}$: Let $k = 1$. Then $\frac{7\pi}{4}- 2\pi=\frac{7\pi}{4}-\frac{8\pi}{4}=-\frac{\pi}{4}

eq\frac{\pi}{4}$.

• For $-\frac{9\pi}{4}$: Let $k = 2$. Then $\frac{7\pi}{4}-2\times2\pi=\frac{7\pi}{4}-\frac{16\pi}{4}=-\frac{9\pi}{4}$.
• For $\frac{11\pi}{4}$: Let $k=-1$. Then $\frac{7\pi}{4}+2\pi=\frac{7\pi + 8\pi}{4}=\frac{15\pi}{4}

eq\frac{11\pi}{4}$.

Answer:

$-\frac{9\pi}{4}$