# im having trouble with this question express all radian measures in terms of pi express -5pi/6 radians in degrees?

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embizze | Certified Educator

There are `2pi` radians in `360^@` . (Imagine a circle of radius 1. The circumference is `pi*d=2pi` -- but radian measure is the distance around the circle.) Then there are `pi` radians in `180^@` .

`pi"radians"=180^@` ``Divide both sides by `pi` :

1 rad = `180^@/pi` Multiply both sides by `(-5pi)/6` :

`(-5pi)/6"rad"=(-5pi)/6*180^@/pi`

`=-150^@`

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