Question

Convert the angle 405 degrees to radians. Give the exact value and use pi for pi.Please show work neatly

Answer 1

Remember that

`360^o=2\pi`

so

Applying proportion

Find out how many radians represent 405 degrees

`\begin{gathered} (2\pi)/(360^o)=(x)/(405^o) \\ solve\text{ for x} \\ x=(2\pi)/(360^(o))*405^o \\ \\ x=(810\pi)/(360) \\ \\ x=(9\pi)/(4)\text{ radians} \end{gathered}`

The answer is 9pi/4 radians