Question

answer the following. (a) find an angle between 0 and 2π that is coterminal with $\frac{13pi}{6}$. (b) find an angle between 0° and 360° that is coterminal with - 240°. give exact values for your answers. (a) radians (b) °

Explanation:

Step1: Subtract full - rotation for radians

To find a coterminal angle of $\frac{13\pi}{6}$ between $0$ and $2\pi$, we know that a full - rotation is $2\pi=\frac{12\pi}{6}$. Subtract $\frac{12\pi}{6}$ from $\frac{13\pi}{6}$.
$\frac{13\pi}{6}-\frac{12\pi}{6}=\frac{\pi}{6}$

Step2: Add full - rotation for degrees

To find a coterminal angle of $- 240^{\circ}$ between $0^{\circ}$ and $360^{\circ}$, we add $360^{\circ}$ to $-240^{\circ}$.
$-240^{\circ}+360^{\circ}=120^{\circ}$

Answer:

(a) $\frac{\pi}{6}$
(b) $120$