Question

ME AJUDEM POR FAVOR
URGENTE!!!!
E POR FAVOR COLOQUEM CÁLCULO

Answer 1

a) pi / 3 = 180 / 3 = 60°
b) pi / 2 = 180 / 2 = 90°
c) pi / 4 = 180 / 4 = 45°
d) pi / 5 = 180 / 5 = 36°
e) 0.5 rad
f) 3pi / 4 = 3 * 180 / 4 = 540 / 4 = 135°
g) 2 pi / 9 = 2 * 180 / 9 = 360 / 9 = 40°
h) 11 pi / 6 = 11 * 180 / 6 = 1980 / 6 = 330°
i) 3 rad

BONS ESTUDOS!

Answer 2

Para transformar de radianos para graus (e vice-versa) usamos as seguintes relações:

$1\text{ rad}=\dfrac{180^{\circ}}{\pi}\;\;\Leftrightarrow\;\;1^{\circ}=\dfrac{\pi}{180}\text{ rad}$


Neste caso, basta multiplicar o arco expresso em radianos por $\dfrac{180^{\circ}}{\pi}$, e obtem-se o seu valor correspondente em graus.


a) $\dfrac{\pi}{3}\text{ rad}$

$=\dfrac{\diagup\!\!\!\! \pi}{3}\cdot \dfrac{180^{\circ}}{\diagup\!\!\!\! \pi}\\ \\ =\dfrac{180^{\circ}}{3}\\ \\ =60^{\circ}$


b) $\dfrac{\pi}{2}\text{ rad}$

$=\dfrac{\diagup\!\!\!\! \pi}{2}\cdot \dfrac{180^{\circ}}{\diagup\!\!\!\! \pi}\\ \\ =\dfrac{180^{\circ}}{2}\\ \\ =90^{\circ}$


c) $\dfrac{\pi}{4}\text{ rad}$

$=\dfrac{\diagup\!\!\!\! \pi}{4}\cdot \dfrac{180^{\circ}}{\diagup\!\!\!\! \pi}\\ \\ =\dfrac{180^{\circ}}{4}\\ \\ =45^{\circ}$


d) $\dfrac{\pi}{5}\text{ rad}$

$=\dfrac{\diagup\!\!\!\! \pi}{5}\cdot \dfrac{180^{\circ}}{\diagup\!\!\!\! \pi}\\ \\ =\dfrac{180^{\circ}}{5}\\ \\ =36^{\circ}$


e) $0,5\text{ rad}$

$=0,5\cdot \dfrac{180^{\circ}}{\pi}\\ \\ =\dfrac{0,5\cdot 180^{\circ}}{\pi}\\ \\ =\dfrac{90,0^{\circ}}{\pi}\\ \\ \simeq 28,6^{\circ}$


f) $\dfrac{3\pi}{4}\text{ rad}$

$=\dfrac{3\diagup\!\!\!\! \pi}{4}\cdot \dfrac{180^{\circ}}{\diagup\!\!\!\! \pi}\\ \\ =\dfrac{3 \cdot 180^{\circ}}{4}\\ \\ =\dfrac{540^{\circ}}{4}\\ \\ =135^{\circ}$


g) $\dfrac{2\pi}{9}\text{ rad}$

$=\dfrac{2\diagup\!\!\!\! \pi}{9}\cdot \dfrac{180^{\circ}}{\diagup\!\!\!\! \pi}\\ \\ =\dfrac{2 \cdot 180^{\circ}}{9}\\ \\ =\dfrac{360^{\circ}}{9}\\ \\ =40^{\circ}$


h) $\dfrac{11\pi}{6}\text{ rad}$

$=\dfrac{11\diagup\!\!\!\! \pi}{6}\cdot \dfrac{180^{\circ}}{\diagup\!\!\!\! \pi}\\ \\ =\dfrac{11 \cdot 180^{\circ}}{6}\\ \\ =\dfrac{1\,980^{\circ}}{6}\\ \\ =330^{\circ}$


i) $3\text{ rad}$

$=3\cdot \dfrac{180^{\circ}}{\pi}\\ \\ =\dfrac{3 \cdot 180^{\circ}}{\pi}\\ \\ =\dfrac{540^{\circ}}{\pi}\\ \\ \simeq 171,9^{\circ}$