Question

convert the angle \\(\frac{19pi}{12}\\) radians to degrees.

Explanation:

Step1: Recall the conversion formula

To convert radians to degrees, we use the formula: Degree measure = Radian measure × $\frac{180^\circ}{\pi}$.

Step2: Substitute the given radian measure

We are given the radian measure as $\frac{19\pi}{12}$. Substituting this into the formula, we get: Degree measure = $\frac{19\pi}{12}$ × $\frac{180^\circ}{\pi}$.

Step3: Simplify the expression

The $\pi$ in the numerator and denominator cancels out. Then we calculate $\frac{19\times180}{12}$. First, simplify $\frac{180}{12}=15$. Then, $19\times15 = 285$. So the degree measure is $285^\circ$.

Answer:

$285^\circ$