Answer:
Correct answers:
A. An angle that measures [tex]\frac{\pi}{6}[/tex] radians also measures [tex]30^o[/tex]
C. An angle that measures [tex]180^o[/tex] also measures [tex]\pi[/tex] radians
Step-by-step explanation:
Recall the formula to transform radians to degrees and vice-versa:
[tex]\angle\,radians=\frac{\pi}{180^o} \,* \,\angle degrees\\ \\\angle\,degrees=\frac{180^o}{\pi} \,* \,\angle radians[/tex]
Therefore we can investigate each of the statements, and find that when we have a [tex]\frac{\pi}{6}[/tex] radians angle, then its degree formula becomes:
[tex]\angle\,degrees=\frac{180^o}{\pi} \,* \,\angle radians\\\angle\,degrees=\frac{180^o}{\pi} \,* \,\frac{\pi}{6} \\\angle\,degrees=\frac{180^o}{6} \\\angle\,degrees=30^o[/tex]
also when an angle measures [tex]180^o[/tex] , its radian measure is:
[tex]\angle\,radians=\frac{\pi}{180^o} \,* \,\angle degrees\\\angle\,radians=\frac{\pi}{180^o} \,* \,180^o\\\angle\,radians=\pi[/tex]
The other relationships are not true as per the conversion formulas
