Question

a) Find a positive angle less than 2𝜋 that is coterminal with 16𝜋 3 radians.

b) Find the reference angle for 16𝜋 3 radians.

Answer 1

Subtract $2\pi$ from $16\pi$

$\Rightarrow$ $\dfrac{16\pi}{3}− 2 π$

The resulting angle of$\dfrac{10\pi}{3}$  is positive, less than $2\pi$ and coterminal with $\dfrac{16\pi}{3}$

$\dfrac{10\pi}{3}$

Subtract$2\pi$ from $\dfrac{10\pi}{3}$

$\dfrac{10\pi}{3}-2\pi$

The resulting angle of $\dfrac{4\pi}{3}$ is positive, less than and coterminal with $\dfrac{16\pi}{3}$

$\dfrac{4\pi}{3}$

Since the angle $\pi$ is in the third quadrant subtract $\pi$ from $\dfrac{4\pi}{3}$

$\Rightarrow \dfrac{\pi}{3}$