QuestionAugust 25, 2025

Which angle is coterminal with -(pi )/(2) -(7pi )/(2) (3pi )/(2) (5pi )/(2)

Which angle is coterminal with -(pi )/(2) -(7pi )/(2) (3pi )/(2) (5pi )/(2)
Which angle is coterminal with -(pi )/(2) -(7pi )/(2) (3pi )/(2) (5pi )/(2)

Solution
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Answer

None of the given angles are coterminal with -\frac{\pi}{2}. Explanation 1. Understand Coterminal Angles Coterminal angles differ by integer multiples of 2\pi. If \theta is an angle, then angles coterminal with it are given by \theta + 2k\pi, where k is an integer. 2. Check Each Angle For each given angle, check if it can be expressed as -\frac{\pi}{2} + 2k\pi for some integer k. - **-\frac{7\pi}{2}:** -\frac{\pi}{2} + 2(-3)\pi = -\frac{\pi}{2} - 6\pi = -\frac{13\pi}{2} (not coterminal) - **\frac{3\pi}{2}:** -\frac{\pi}{2} + 2(2)\pi = -\frac{\pi}{2} + 4\pi = \frac{7\pi}{2} (not coterminal) - **\frac{5\pi}{2}:** -\frac{\pi}{2} + 2(3)\pi = -\frac{\pi}{2} + 6\pi = \frac{11\pi}{2} (not coterminal) 3. Verify Calculation Re-evaluate calculations to ensure accuracy. None of the given angles match -\frac{\pi}{2} + 2k\pi.

Explanation

1. Understand Coterminal Angles<br /> Coterminal angles differ by integer multiples of $2\pi$. If $\theta$ is an angle, then angles coterminal with it are given by $\theta + 2k\pi$, where $k$ is an integer.<br />2. Check Each Angle<br /> For each given angle, check if it can be expressed as $-\frac{\pi}{2} + 2k\pi$ for some integer $k$.<br />- **$-\frac{7\pi}{2}$:** $-\frac{\pi}{2} + 2(-3)\pi = -\frac{\pi}{2} - 6\pi = -\frac{13\pi}{2}$ (not coterminal)<br />- **$\frac{3\pi}{2}$:** $-\frac{\pi}{2} + 2(2)\pi = -\frac{\pi}{2} + 4\pi = \frac{7\pi}{2}$ (not coterminal)<br />- **$\frac{5\pi}{2}$:** $-\frac{\pi}{2} + 2(3)\pi = -\frac{\pi}{2} + 6\pi = \frac{11\pi}{2}$ (not coterminal)<br /><br />3. Verify Calculation<br /> Re-evaluate calculations to ensure accuracy. None of the given angles match $-\frac{\pi}{2} + 2k\pi$.
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