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

Explanation:

Step1: Convert degrees to radians

We know that to convert degrees to radians, we use the formula $\text{radians}=\frac{\pi}{180}\times\text{degrees}$. So, $60^{\circ}=\frac{\pi}{180}\times60=\frac{\pi}{3}$ and $255^{\circ}=\frac{\pi}{180}\times255=\frac{17\pi}{12}$.

Step2: Compare the values

We have $\frac{3\pi}{10}\approx0.3\pi$, $\frac{\pi}{3}\approx0.33\pi$, $\frac{\pi}{2} = 0.5\pi$, $\frac{2\pi}{3}\approx0.67\pi$, $\frac{17\pi}{12}\approx1.42\pi$. Arranging $\frac{3\pi}{10},\frac{\pi}{3},\frac{\pi}{2},\frac{2\pi}{3},\frac{17\pi}{12}$ from least - to greatest gives $\frac{3\pi}{10},\frac{\pi}{3},\frac{\pi}{2},\frac{2\pi}{3},\frac{17\pi}{12}$. Since $\frac{\pi}{3}=60^{\circ}$ and $\frac{17\pi}{12} = 255^{\circ}$, the correct order from least to greatest is $\frac{3\pi}{10},60^{\circ},\frac{\pi}{2},\frac{2\pi}{3},255^{\circ}$.

Answer:

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