Question

Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by two.

three pi divided by two; negative pi divided by two
pi divided by two + 360°; pi divided by two - 360°
five pi divided by two; negative pi divided by two
five pi divided by two; negative three pi divided by two

Answer 1

By definition, the angles coterminal with $\alpha$ are: $\alpha +360\degree$ and $\alpha -360\degree$ .(or $\alpha +2\pi$ and $\alpha -2\pi)$

1. $\dfrac{\pi}{2} + 2\pi = \dfrac{5\pi}{2}; \quad \dfrac{\pi}{2} - 2\pi = -\dfrac{3\pi}{2}$
2. $\dfrac{3\pi}{2} + 2\pi = \dfrac{7\pi}{2}; \quad \dfrac{3\pi}{2} - 2\pi = -\dfrac{\pi}{2}$
3. $-\dfrac{\pi}{2} + 2\pi = \dfrac{3\pi}{2}; \quad -\dfrac{\pi}{2} - 2\pi = -\dfrac{5\pi}{2}$
4. $\dfrac{\pi}{2} +2\pi+ 2\pi = \dfrac{9\pi}{2}; \quad \dfrac{\pi}{2} +2\pi - 2\pi = \dfrac{\pi}{2}$
5. $\dfrac{\pi}{2} -2\pi+ 2\pi = \dfrac{\pi}{2}; \quad \dfrac{\pi}{2} -2\pi - 2\pi = -\dfrac{7\pi}{2}$
6. $\dfrac{5\pi}{2} + 2\pi = \dfrac{9\pi}{2}; \quad \dfrac{5\pi}{2} - 2\pi = \dfrac{\pi}{2}$
7. $-\dfrac{\pi}{2} + 2\pi = \dfrac{3\pi}{2}; \quad -\dfrac{\pi}{2} - 2\pi = -\dfrac{5\pi}{2}$
8. $-\dfrac{3\pi}{2} + 2\pi = \dfrac{\pi}{2}; \quad - \dfrac{3\pi}{2} - 2\pi = -\dfrac{7 \pi}{2}$