What is $\frac{- 4 π}{3}$ $(-4pi)/3$ radians in degrees?

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What is $\frac{- 4 π}{3}$ $(-4pi)/3$ radians in degrees?

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Answer 1 · 2015-12-10T21:31:11

Recall:
$360^{\circ} = 2 π$ $360^@=2pi$ $r a d i a n s$ $radians$ , $180^{\circ} = π$ $180^@=pi$ $r a d i a n s$ $radians$

To convert $\frac{- 4 π}{3}$ $(-4pi)/3$ to degrees, multiply the fraction by $\frac{180^{\circ}}{π}$ $180^@/pi$ . Keep in mind that $\frac{180^{\circ}}{π}$ $180^@/pi$ has a value of $1$ $1$ , so the answer does not change. Instead, only the units are changed:

$\frac{- 4 π}{3} \cdot \frac{180^{\circ}}{π}$ $(-4pi)/3 * 180^@/pi$

$=(-4color(red)cancelcolor(black)pi)/color(green)cancelcolor(black)3 * color(green)cancelcolor(black)(180^@)^(60^@)/color(red)cancelcolor(black)pi$

$=-4*60^@$

$=-240^@$

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What is $\frac{- 4 π}{3}$ $(-4pi)/3$ radians in degrees?

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