Question

(a) Find an angle between 0 and 2π that is coterminal with −19π10.

Answer 1

`(\pi)/(10)`.

Explanation:

All coterminal angles of an angle
`\theta` are defined as

`\theta +2n\pi` or
`\theta + n360^(\circ)`

where, n is an integer.

The given angle is

`\theta=-(19\pi)/(10)`

So, all coterminal angles of an angle
`\theta` are

`-(19\pi)/(10)+2n\pi`

For n=1,

`\Rightarrow -(19\pi)/(10)+2(1)\pi`

`\Rightarrow -(19\pi)/(10)+2\pi`

`\Rightarrow (-19\pi+20\pi)/(10)`

`\Rightarrow (1\pi)/(10)`

Since,
`(\pi)/(10)` between 0 and 2π, therefore, the required coterminal angle is
`(\pi)/(10)`.