Question

Convert the following angle from degrees to radians. express your answer in simplest form.show work

Answer 1

$\begin{gathered} In\text{ fraction: }x\text{ =}\frac{4\pi rad}{3} \\ In\text{ decimal: x = 4.1867} \end{gathered}$Explanation:

Conversion from degrees to radians:

1 π rad = 180 degrees

if degree is 240,

let x = amount in rad

180 degrees = 1 π rad

240 degrees = x

cross multiply:

x(180) = 240(1 π rad )

180x = 240π rad

divide both sides by 180:

180x/180 = 240π rad/180

$\begin{gathered} x=\frac{240\pi rad}{180} \\ x\text{ =}\frac{4\pi rad}{3} \end{gathered}$

In decimal:

$\begin{gathered} x\text{ =}\frac{4\pi rad}{3},\text{ if }\pi=\text{ 3.14} \\ x\text{ = }4.1867 \end{gathered}$