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How do you convert the following angle measurements in degrees into radians? $630^{\circ}, 195^{\circ}, - 330^{\circ}, 165^{\circ}$ $630^circ, 195^circ,-330^circ,165^circ$

1 Answer

Feb 6, 2017

(see below)

Explanation:

A complete circle is $360^{\circ}$ $360^@$ or $2 π$ $2pi$ radians.

Therefore $360^{\circ} = 2 π$ $360^@=2pi$ (radians)

$\to XXXXX 1^{\circ} = \frac{2 π}{360}$ $rarrcolor(white)("XXXXX")1^@=(2pi)/360$ (radians)#

1) $XXX 630^{\circ} = 630 \times \frac{2 π}{180} = 7 π$ $color(white)("XXX")630^@=630xx(2pi)/180 = 7pi$ (radians)#

2) $XXX 195^{\circ} = 195 \times \frac{2 π}{360} = \frac{13}{6} π$ $color(white)("XXX")195^@=195xx(2pi)/360=13/6pi$ (radians)

3) $XXX - 330^{\circ} = (- 330) \times \frac{2 π}{360} = (- \frac{11}{6}) π$ $color(white)("XXX")-330^@=(-330)xx(2pi)/360=(-11/6)pi$ (radians)

4) $XXX 165^{\circ} = 165 \times \frac{2 π}{360} = \frac{11}{30} π$ $color(white)("XXX")165^@=165xx(2pi)/360=11/30pi$ (radians)

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