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 gonna convert this angle negative five pi over six, which is given to us in radians, and we wanna 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 one eighty or one eighty over pi. Alright? So if I wanna go from negative five pi over six 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 one eighty or one eighty over pi? Well, hopefully, you guessed that it's gonna be one eighty 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 one eighty over pi. Alright? So what you'll see here is that the pi's 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 one eighty times negative five over six. 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 one eighty over six 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 five, 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, 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°

12. Trigonometric Functions

Angles

Business Calculus

12. Trigonometric Functions

Angles

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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

Step 1: Recall the formula for converting radians to degrees: $ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} $. This formula helps us convert an angle given in radians to its equivalent in degrees.

Step 2: Substitute the given angle $ -\frac{5\pi}{6} $ into the formula. The calculation becomes $ \text{Degrees} = -\frac{5\pi}{6} \times \frac{180}{\pi} $.

Step 3: Simplify the expression by canceling $ \pi $ in the numerator and denominator. This leaves $ \text{Degrees} = -\frac{5}{6} \times 180 $.

Step 4: Perform the multiplication $ -\frac{5}{6} \times 180 $. This involves multiplying $ 180 $ by $ -5 $ and then dividing the result by $ 6 $.

Step 5: The result of the calculation gives the angle in degrees. Compare this value to the provided options ($ -120\degree $, $ -150\degree $, $ -210\degree $, $ -240\degree $) to identify the correct answer.

5:50m

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