Answer to Question #97670 in Calculus for Katya Drayton

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. $-\dfrac{3\pi}{2} + 2\pi = \dfrac{\pi}{2}; \quad - \dfrac{3\pi}{2} - 2\pi = -\dfrac{7 \pi}{2}$