Question

convert the radian measure to degrees. 2 2 radian(s) = ° (round to the nearest minute.)

Explanation:

Step1: Recall conversion formula

We know that to convert radians to degrees, we 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 $R = 2$.
So $D=2\times\frac{180^{\circ}}{\pi}=\frac{360^{\circ}}{\pi}\approx 114.591559^{\circ}$.

Step2: Separate degrees and minutes

The whole - number part of the degree measure is the degree value. $114.591559^{\circ}=114^{\circ}+0.591559^{\circ}$.
To convert the decimal part of the degree to minutes, we use the conversion $1^{\circ} = 60'$. So the number of minutes $m=0.591559\times60\approx 35.49354$. Rounding to the nearest minute, $m\approx 35'$.

Answer:

$114^{\circ}35'$