Convert the angle −5π6-\frac{5\pi}{6}−65π from radians to degrees.

− 150 ° -150\degree − 150°

Convert the angle − 5 π 6 -\frac{5\pi}{6} − 6 5 π from radians to degrees .

Everyone, so let's just jump right into this practice problem here. We're going to convert this angle negative 5pisix, which is given to us in radians, and we want to express this in terms of degrees. So we know what we're gonna do, we're gonna use our conversion equations. We're gonna multiply either by pi over 180 or 180 over pi. Alright? So if I wanna go from negative 5 pi over 6 radians, and I wanna end up with something that's in degrees over here, then what I'm gonna have to do is I'm gonna have to multiply by whatever is gonna get rid of the radians and leave me with degrees. So what is that fraction? Is it pi over 180 or 180 over pi? Well, hopefully, you guess that it's gonna be 180 over pi, because you can see here that the pis will cancel if you do this, and the radians will cancel if you do this. So you have to multiply by 180 over pi. Alright? So what you'll see here is the pis will usually cancel in these, in these types of things. That's that's awesome. And what we're gonna see here is that the radians will cancel. So, we were left with 180 times negative five over 6. Now there's a couple of different ways you can do this. You can multiply this out on the numerator and then just work this out on your calculators, but you can also just see here that 180 over 6 is a little bit of an easier sort of division, and that actually just leaves you with 30. So this is basically like 30 times negative 5, and what this will end up getting you is, this will end up getting you negative 150 degrees. So that is the answer. It's negative 150 degrees. So just as with positive values that you can convert between radians and degrees, you can also do the same thing for negative values, and that's perfectly fine. Alright? So, let me know if you have any questions. Thanks for watching.

Convert the angle − 5 π 6 -\frac{5\pi}{6} − 6 5 π from radians to degrees .

− 150 ° -150\degree − 150°

− 120 ° -120\degree − 120°

− 210 ° -210\degree − 210°

− 240 ° -240\degree − 240°

1. Measuring Angles

Radians

Trigonometry

1. Measuring Angles

Radians

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Multiple Choice

Convert the angle $-\frac{5\pi}{6}$ from radians to degrees.

$-120\degree$

$-150\degree$

$-210\degree$

$-240\degree$

Verified step by step guidance

Start by recalling the conversion factor between radians and degrees: 180° is equivalent to π radians.

To convert an angle from radians to degrees, multiply the radian measure by the conversion factor $ \frac{180°}{\pi} $.

Apply this conversion to the given angle $ -\frac{5\pi}{6} $ radians: $ -\frac{5\pi}{6} \times \frac{180°}{\pi} $.

Simplify the expression by canceling out $ \pi $ in the numerator and denominator, resulting in $ -\frac{5 \times 180°}{6} $.

Calculate the multiplication and division to find the degree measure of the angle.

5:4m

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