Question

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

Answer 1

Answer:

$\dfrac{\pi}{10}$.

Step-by-step 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

$\theta=-\dfrac{19\pi}{10}$

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

$-\dfrac{19\pi}{10}+2n\pi$

For n=1,

$\Rightarrow -\dfrac{19\pi}{10}+2(1)\pi$

$\Rightarrow -\dfrac{19\pi}{10}+2\pi$

$\Rightarrow \dfrac{-19\pi+20\pi}{10}$

$\Rightarrow \dfrac{1\pi}{10}$

Since,  $\dfrac{\pi}{10}$  between 0 and 2π, therefore,  the required coterminal angle is $\dfrac{\pi}{10}$.