Questions: Question 2 Convert the angle in radians to degrees. -11π/12 -166° -164° -165° -167°

Question 2 Convert the angle in radians to degrees. -11π/12 -166° -164° -165° -167°
Transcript text: Question 2 Convert the angle in radians to degrees. \[ -\frac{11 \pi}{12} \] $-166^{\circ}$ $-164^{\circ}$ $-165^{\circ}$ $-167^{\circ}$
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Solution

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Solution Steps

Step 1: Understand the Problem

We need to convert the angle given in radians, −11π12-\frac{11 \pi}{12}, to degrees. We are provided with four multiple-choice options for the degree measure.

Step 2: Conversion Formula

The formula to convert radians to degrees is: Degrees=Radians×180π \text{Degrees} = \text{Radians} \times \frac{180}{\pi}

Step 3: Apply the Conversion

Substitute −11π12-\frac{11 \pi}{12} into the conversion formula: Degrees=−11π12×180π \text{Degrees} = -\frac{11 \pi}{12} \times \frac{180}{\pi}

Step 4: Simplify the Expression

Cancel out π\pi and simplify: Degrees=−11×18012 \text{Degrees} = -\frac{11 \times 180}{12}

Calculate the multiplication and division: Degrees=−198012=−165 \text{Degrees} = -\frac{1980}{12} = -165

Final Answer

The angle in degrees is −165∘-165^\circ. Therefore, the correct multiple-choice answer is: −165∘ \boxed{-165^\circ}

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