Question

Which of the following are in the correct order from least to greatest?

• A. $2\mathrm{\pi },\frac{7\mathrm{\pi }}{6},80°,\frac{\mathrm{\pi }}{4},38°$
• B. $38°,80°,\frac{\mathrm{\pi }}{4},\frac{7\mathrm{\pi }}{6},2\mathrm{\pi }$
• C. $38°,\frac{\mathrm{\pi }}{4},80°,\frac{7\mathrm{\pi }}{6},2\mathrm{\pi }$
• D. $2\mathrm{\pi },38°,80°,\frac{\mathrm{\pi }}{4},\frac{7\mathrm{\pi }}{6}$

Answer 1

The correct option is C

$38°,\frac{\mathrm{\pi }}{4},80°,\frac{7\mathrm{\pi }}{6},2\mathrm{\pi }$

Explanation for correct option:

It is known that the value of $\mathrm{\pi }$ is $180°$. Then the measure of the angles are

$$\begin{gathered} \frac{\mathrm{\pi }}{4}=\frac{180°}{4}\left[\mathrm{Substitute}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{\pi }\right] \\ \therefore \frac{\mathrm{\pi }}{4}=45° \end{gathered}$$

$$\begin{gathered} \frac{7\mathrm{\pi }}{6}=\frac{7\times 180°}{6}\left[\mathrm{Substitute}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{\pi }\right] \\ \Rightarrow \frac{7\mathrm{\pi }}{6}=\frac{7\times 6\times 30°}{6} \\ \Rightarrow \frac{7\mathrm{\pi }}{6}=7\times 30° \\ \therefore \frac{7\mathrm{\pi }}{6}=210° \end{gathered}$$

$$\begin{gathered} 2\mathrm{\pi }=2\times 180°\left[\mathrm{Substitute}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{\pi }\right] \\ \therefore 2\mathrm{\pi }=360° \end{gathered}$$

Then the measure of the angles $38°,\frac{\mathrm{\pi }}{4},80°,\frac{7\mathrm{\pi }}{6},2\mathrm{\pi }$ are $38°,45°,80°,210°,360°$, which are in the correct order from least to greatest.

Therefore, option (C) is correct option.

Hence, the correct answer is option (C).