Question

Find a positive angle less than one revolution around the unit circle that is co-terminal with the given angle: 52π/5

Answer 1

The required angle is
`(2\pi)/(5)`

Explanation

The given angle is
`(52\pi)/(5)`.

To find a positive angle which is coterminal with
`(52\pi)/(5)` and is less than one revolution,

we subtract multiples of
`2\pi` until we obtain an angle between
`0\leq \theta\leq 2\pi`.

Let the positive angle less than one revolution that is coterminal with
`(52\pi)/(5)` be
`\theta`, then

`\theta=(52\pi)/(5)-5(2\pi)`,

We simplify to get,

`\theta=(52\pi)/(5)-10\pi`

We collect LCM to obtain,

`\theta=(52\pi-50\pi)/(5)`

`\theta=(2\pi)/(5)`

The correct answer is A