Question

convert the following radian measure to degree measure
\\(\frac{4\pi}{3}\\)

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 $\frac{4\pi}{3}$. Substitute this into the formula:
Degree measure = $\frac{4\pi}{3}$ × $\frac{180^\circ}{\pi}$

Step3: Simplify the expression

The $\pi$ in the numerator and denominator cancels out. Then we have $\frac{4}{3}$ × $180^\circ$. Calculate $\frac{4\times180^\circ}{3}$ = $4\times60^\circ$ = $240^\circ$.

Answer:

$240^\circ$