The number of radians in a 720^circ angle can be written as api where a is a constant. What is the value of a? square

To find the value of \( a \) in the expression \( 720^\circ = a\pi \) radians, we need to convert degrees to radians.<br /><br />The conversion factor between degrees and radians is:<br />\[ 1 \text{ degree} = \frac{\pi}{180} \text{ radians} \]<br /><br />So, to convert \( 720^\circ \) to radians, we multiply by the conversion factor:<br />\[ 720^\circ \times \frac{\pi}{180} \]<br /><br />Now, perform the multiplication:<br />\[ 720 \times \frac{\pi}{180} = \frac{720\pi}{180} \]<br /><br />Simplify the fraction:<br />\[ \frac{720\pi}{180} = 4\pi \]<br /><br />Therefore, \( 720^\circ \) is equal to \( 4\pi \) radians. Hence, the value of \( a \) is:<br />\[ a = 4 \]<br /><br />So, the answer is:<br />\[ \boxed{4} \]