Question

Determine the angle between 0 and 2π that is coterminal with quantity
`(19\pi )/(4\\)`


`(11\pi )/(4) \\\\(5\pi )/(4) \\\\(3\pi )/(4) \\\\(\pi )/(4)`

Answer 1

`(3\pi)/(4)`

Explanation:

Recall that co-terminal angles are angles which when drawn at standard position share a terminal side. Since we are restricted to the interval [0,2π], recognize that
`(19\pi)/(4)=(16\pi)/(4)+(3\pi)/(4)=4\pi+(3\pi)/(4)=2\pi+2\pi+(3\pi)/(4)=(3\pi)/(4)`. So, the co-terminal angle is
`(3\pi)/(4)`.