Defining key terms related to circles

How many radians does a circle have?

• 360 degrees

• $2\pi$ radians

• $\pi$ radians

• ^{2 radians}

What is 7π/10 in degrees?

• 120

• 126

• 123

• 119

Convert 300° to a radian measure.

Convert 12^o21'8'' to decimal degrees. Round to the nearest hundredth of a degree.

• 12.35

• 8.35

• 12.78

• 21.22

Please give the degree measure angle equivalent to $\pi$  radians. Your answer will be an integer number of degrees, for example "75".

Answer explanation

An angle measuring around the circle is  $2\pi$  radians, or 360 degrees.  Half that is  $\pi$  radians or 180 degrees, which is your answer.  The easiest way to find the answer is probably mental math, rather than using the proportion  $\frac{\pi}{180}=\frac{\theta R}{\theta\degree}$  .

What is the equivalent degree measure of  $\frac{4\pi}{3}$  

• 150

• 240

• 270

• 300

 $convert\ \frac{2\pi}{3}\ to\ \deg rees$  

•  $120\degree$  

•  $180\degree$  

•  $225\degree$  

•  $23\degree$  

What is  $225\degree$   in radians? 

•  $\frac{7\pi}{4}$  

•  $\frac{5\pi}{4}$  

•  $\frac{3\pi}{4}$  

•  $\frac{5\pi}{3}$