Circles and conic sections

What 180° is equal to?

• 2pi radians

• 1 radian

• Pi radian

• 0.2 radians

Please give the radian measure angle equivalent to  $90\degree$ .

•  $\frac{\pi}{2}$  radians, or about 1.57 radians.

•  $\frac{\pi}{4}$  radians, or about 0.79 radians.

•  $2\pi$  radians, or about 6.28 radians.

•  $\frac{3\pi}{4}$  radians, or about 2.36 radians.

Answer explanation

 $90\degree$  is one-fourth of the degree-angle measuring around the whole circle ( $360\degree$  ), so  $\frac{\pi}{2}$  radians is the answer because it is one-fourth of the radian-angle measuring around the whole circle ( $2\pi$  ).  Again, mental math is probably easier than using the proportion  $\frac{\pi}{180}=\frac{\theta R}{\theta\degree}$   .

Convert 120° to pi radians

Mathematical Equivalence

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What is 240 degrees in radians? 

What is π/3 radians in degrees? 

• 30
• 60
• 360
• 90

What is 60 degrees in radians? 

• 2π/3
• π/3
• 4π/3
• π/6

Convert  $110\degree$  into radians

•  $\frac{5\pi}{3}$  

•  $\frac{3\pi}{4}$  

•  $\frac{11\pi}{18}$  

•  $\frac{11\pi}{9}$  

Convert to degrees

• -270 degrees

• -135 degrees

• -130 degrees

• -140 degrees

Convert - 13π / 6 radians into degrees

• -330^o

• -390^o

• -300^o

• -315^o

Convert to radians: 210°

• 3π/6
• 7π/6
• 7π/3
• 6π/7