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

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

Answer:

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

Explanation:

Step1: Convert radians to degrees

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

Step2: Compare the values

We have $38^{\circ},45^{\circ},80^{\circ},210^{\circ},360^{\circ}$. In ascending - order: $38^{\circ},45^{\circ}(=\frac{\pi}{4}),80^{\circ},210^{\circ}(=\frac{7\pi}{6}),360^{\circ}( = 2\pi)$.