Converting Between Radians and Degrees

What is 60 degrees in radians? 

• 2π/3

• π/3

• 4π/3

• π/6

Convert 510^o to Radians

• 25π / 3

• 23π / 8

• 17π / 6

• 51π / 8

How confident are you in converting between degrees and radian measures?

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Which is the correct conversion factor to use when converting from DEGREES TO RADIANS?

• 180^o/π rad

• π rad / 180^o

• π rad / 360^o

• ^360o/π rad

Convert 150⁰ to radians

Answer explanation

 $\frac{\pi}{6}=30\degree$  , so  $-\frac{\pi}{6}=-30\degree$  .  Using the proportion,  $\frac{\pi}{180}=\frac{-\frac{\pi}{6}}{\theta\degree}$  , so  $\theta\degree=\frac{-\frac{\pi}{6}\cdot180}{\pi}=-30\degree$  .

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  $\frac{\pi}{180}=\frac{\theta R}{\theta\degree}$  .

Answer explanation

Since $\frac{\pi}{4}$  radians is  $45\degree$  , three times that is your answer,  $135\degree$ .  You can also use the proportion,  $\frac{\pi}{180}=\frac{\left(\frac{3\pi}{4}\right)}{\theta\degree}$  and solve for  $\theta\degree$  .   $\theta\degree=\frac{\frac{3\pi}{4}\cdot180}{\pi}$  or $135\degree$ .

Answer explanation

 $\frac{\pi}{3}=60\degree$  , so  $\frac{2\pi}{3}=120\degree$  .  Using the proportion  $\frac{\pi}{180}=\frac{\frac{2\pi}{3}}{\theta\degree}$  ,  $\theta\degree=\frac{\frac{2\pi}{3}\cdot180}{\pi}=120\degree$