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, \(-\frac{11 \pi}{12}\), 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: \[ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \]

Step 3: Apply the Conversion

Substitute \(-\frac{11 \pi}{12}\) into the conversion formula: \[ \text{Degrees} = -\frac{11 \pi}{12} \times \frac{180}{\pi} \]

Step 4: Simplify the Expression

Cancel out \(\pi\) and simplify: \[ \text{Degrees} = -\frac{11 \times 180}{12} \]

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

Final Answer

The angle in degrees is \(-165^\circ\). Therefore, the correct multiple-choice answer is: \[ \boxed{-165^\circ} \]

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