Questions: Convert the angle in radians to degrees. -5π/6 -5π/6 = - (Simplify your answer.)

Transcript text: Convert the angle in radians to degrees. \[ -\frac{5 \pi}{6} \] $-\frac{5 \pi}{6}=$ $\square$ - (Simplify your answer.)

Solution

Solution Steps

To convert an angle from radians to degrees, we use the conversion factor $ \frac{180}{\pi} $. Multiply the given angle in radians by this factor to get the angle in degrees.

Step 1: Convert Radians to Degrees

To convert the angle $ -\frac{5\pi}{6} $ radians to degrees, we use the conversion formula: \[ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \] Substituting the given value: \[ \text{Degrees} = -\frac{5\pi}{6} \times \frac{180}{\pi} \]

Step 2: Simplify the Expression

The $ \pi $ in the numerator and denominator cancels out: \[ \text{Degrees} = -\frac{5 \times 180}{6} \] Calculating the multiplication and division: \[ \text{Degrees} = -\frac{900}{6} = -150 \]