Exercises - The Measurement of Angles

  1. Draw the each given angle in standard position:

    1. $60^{\circ}$   $\ians{}$

    2. $135^{\circ}$   $\ians{}$

    3. $1140^{\circ}$   $\ians{}$

    4. $-240^{\circ}$   $\ians{}$

    5. $\displaystyle{\frac{\pi}{3}}$   $\ians{}$

    6. $\displaystyle{\frac{7\pi}{6}}$   $\ians{}$

    7. $\displaystyle{-\frac{\pi}{6}}$   $\ians{}$

    8. $\displaystyle{\frac{5\pi}{2}}$   $\ians{}$

  2. Convert from degrees to radians:

    1. $45^{\circ}$   $\ans{\displaystyle{\frac{\pi}{4}}}$

    2. $270^{\circ}$   $\ans{\displaystyle{\frac{3\pi}{2}}}$

    3. $1^{\circ}$   $\ans{\displaystyle{\frac{\pi}{180}}}$

    4. $-230^{\circ}$   $\ans{\displaystyle{-\frac{23\pi}{18}}}$

    5. $540^{\circ}$   $\ans{\displaystyle{3\pi}}$

  3. Convert from radians to degrees:

    1. $\displaystyle{\frac{2\pi}{3}}$   $\ans{\displaystyle{120^{\circ}}}$

    2. $7\pi$   $\ans{\displaystyle{1260^{\circ}}}$

    3. $\displaystyle{\frac{\pi}{6}}$   $\ans{\displaystyle{30^{\circ}}}$

    4. $\displaystyle{\frac{19\pi}{2}}$   $\ans{\displaystyle{1710^{\circ}}}$