Question

convert the following radian measure to degrees. - 3.08168 - 3.08168 radians = (round to the nearest minute as needed.)

Explanation:

Step1: Recall conversion formula

To convert radians to degrees, use the formula $D = R\times\frac{180^{\circ}}{\pi}$, where $D$ is the measure in degrees and $R$ is the measure in radians. Here $R=- 3.08168$.
\[D=-3.08168\times\frac{180^{\circ}}{\pi}\]

Step2: Calculate degree - value

\[D=\frac{-3.08168\times180}{\pi}\approx\frac{- 554.7024}{\pi}\approx - 176.57^{\circ}\]

Step3: Separate whole - degrees and decimal part

The whole - degree part is $-176^{\circ}$. The decimal part is $0.57^{\circ}$.

Step4: Convert decimal degrees to minutes

Since $1^{\circ}=60'$, then the number of minutes is $0.57\times60 = 34.2'$. Rounding to the nearest minute gives $34'$.

Answer:

$-176^{\circ}34'$