Radian Measure and the Unit Circle

Check all that apply regarding facts (or definitions) of radian measurement of angles.

• 360 radians in a full rotation.

•  $2\pi$  radians in a full rotation.

•  $\theta=\frac{S}{r}$  therefore we can also say  $S=r\cdot\theta$  

•  $radians=\frac{intercepted\ arclength\ of\ a\ central\ angle}{radius\ length}$  

•  $180$  radians is half a full rotation.

Check all that apply regarding facts (or definitions) of radian measurement of angles.

• $360\degree=2\pi$

• $180\degree=\pi$

• $1\degree=\frac{\pi}{180}$

• $\frac{180\degree}{\pi}=1\ radian\approx57.3\degree$

• $2\ radians\approx114.6\degree$

 $m\angle\theta=4\$  lies in Quadrant ____________.

• Quadrant I

• Quadrant II
  

• Quadrant III

• Quadrant IV

Approximate the radian measurement of  $\theta$  .

• 2 radians

• 3 radians

• 4 radians

• 5 radians

• 6 radians

What is the radian measurement of  $\theta$  ?

•  $-\frac{\pi}{2}$  

•  $\frac{\pi}{2}$  

•  $-\frac{3\pi}{2}$  

•  $\frac{3\pi}{2}$  

 $\sin\left(\frac{\pi}{2}\right)=$  

• 1

• -1

• 0

• UNDEFINED

 $\cos\left(\frac{\pi}{2}\right)=$  

• 1

• -1

• 0

• UNDEFINED

 $\frac{3\pi}{4}$  lies in  _____ and has a reference angle of _____ .

• Quadrant II,  $\frac{\pi}{3}$  

• Quadrant II,  $\frac{\pi}{4}$  

• Quadrant II,  $\frac{\pi}{6}$  

Convert  $\frac{5\pi}{3}$  to degrees

•  $270\degree$  

•  $300\degree$  

•  $315\degree$  

•  $330\degree$  

You are converting  $54\degree$  to radians.  What is the best strategy and radian measurement?

• multiply by  $\frac{180\degree}{\pi}$  which gives the radian measurement of  $3,094$  

• multiply by  $\frac{\pi}{180}$  which gives the radian measurement of  $\frac{3\pi}{10}$  

• multiply by  $\pi$  which gives a radian measurement of  $54\pi$  

• multiply by  $\frac{\pi}{2}$  which gives a radian measurement of  $27\pi$