which of the following are in the correct order from least to greatest?\n$\frac{3pi}{10}$, $60^{circ}$…

which of the following are in the correct order from least to greatest?\n$\frac{3pi}{10}$, $60^{circ}$, $\frac{pi}{2}$, $\frac{2pi}{3}$, $255^{circ}$\n$255^{circ}$, $\frac{2pi}{3}$, $\frac{pi}{2}$, $60^{circ}$, $\frac{3pi}{10}$\n$\frac{3pi}{10}$, $\frac{pi}{2}$, $\frac{2pi}{3}$, $60^{circ}$, $255^{circ}$\n$255^{circ}$, $60^{circ}$, $\frac{2pi}{3}$, $\frac{pi}{2}$, $\frac{3pi}{10}$

which of the following are in the correct order from least to greatest?\n$\frac{3pi}{10}$, $60^{circ}$, $\frac{pi}{2}$, $\frac{2pi}{3}$, $255^{circ}$\n$255^{circ}$, $\frac{2pi}{3}$, $\frac{pi}{2}$, $60^{circ}$, $\frac{3pi}{10}$\n$\frac{3pi}{10}$, $\frac{pi}{2}$, $\frac{2pi}{3}$, $60^{circ}$, $255^{circ}$\n$255^{circ}$, $60^{circ}$, $\frac{2pi}{3}$, $\frac{pi}{2}$, $\frac{3pi}{10}$

Answer

Explanation:

Step1: Convert angles to same - type

Convert all angles to degrees. Recall that to convert radians to degrees, use the formula $\text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}$.

  • $\frac{3\pi}{10}\text{ radians}=\frac{3\pi}{10}\times\frac{180^{\circ}}{\pi}=54^{\circ}$
  • $\frac{\pi}{2}\text{ radians}=\frac{\pi}{2}\times\frac{180^{\circ}}{\pi}=90^{\circ}$
  • $\frac{2\pi}{3}\text{ radians}=\frac{2\pi}{3}\times\frac{180^{\circ}}{\pi}=120^{\circ}$
  • We already have $60^{\circ}$ and $255^{\circ}$ in degrees.

Step2: Arrange in ascending - order

Arrange the angles $54^{\circ},60^{\circ},90^{\circ},120^{\circ},255^{\circ}$ in ascending - order. The order is $54^{\circ}(=\frac{3\pi}{10}),60^{\circ},\frac{\pi}{2}( = 90^{\circ}),\frac{2\pi}{3}(=120^{\circ}),255^{\circ}$

Answer:

$\frac{3\pi}{10},60^{\circ},\frac{\pi}{2},\frac{2\pi}{3},255^{\circ}$