which of the following are in the correct order from least to greatest?\n$2pi$, $\frac{7pi}{6}$…

which of the following are in the correct order from least to greatest?\n$2pi$, $\frac{7pi}{6}$, $80^{circ}$, $\frac{pi}{4}$, $38^{circ}$\n$38^{circ}$, $80^{circ}$, $\frac{pi}{4}$, $\frac{7pi}{6}$, $2pi$\n$38^{circ}$, $\frac{pi}{4}$, $80^{circ}$, $\frac{7pi}{6}$, $2pi$\n$2pi$, $38^{circ}$, $80^{circ}$, $\frac{pi}{4}$, $\frac{7pi}{6}$

which of the following are in the correct order from least to greatest?\n$2pi$, $\frac{7pi}{6}$, $80^{circ}$, $\frac{pi}{4}$, $38^{circ}$\n$38^{circ}$, $80^{circ}$, $\frac{pi}{4}$, $\frac{7pi}{6}$, $2pi$\n$38^{circ}$, $\frac{pi}{4}$, $80^{circ}$, $\frac{7pi}{6}$, $2pi$\n$2pi$, $38^{circ}$, $80^{circ}$, $\frac{pi}{4}$, $\frac{7pi}{6}$

Answer

Explanation:

Step1: Convert radians to degrees

Use the formula $1\text{ rad}=\frac{180^{\circ}}{\pi}$. So, $\frac{\pi}{4}=\frac{180^{\circ}}{4}=45^{\circ}$, $\frac{7\pi}{6}=\frac{7\times180^{\circ}}{6} = 210^{\circ}$, $2\pi=360^{\circ}$.

Step2: Compare the values

We have $38^{\circ},45^{\circ},80^{\circ},210^{\circ},360^{\circ}$ which correspond to $38^{\circ},\frac{\pi}{4},80^{\circ},\frac{7\pi}{6},2\pi$.

Answer:

C. $38^{\circ},\frac{\pi}{4},80^{\circ},\frac{7\pi}{6},2\pi$