<s>[INST] Give $3$ coterminal angles 
Give three angle measures in radians which are coterminal with each of the following. Include at least one positive and one negative angle measure.



*

*$$\pi/4\quad \text{rad}$$

*$$5\pi/3\quad \text{rad}$$
 [/INST] Firstly let us have a look at the definition of coterminal:

Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.


The angles can be anything as long as the lines are aligned. Here are some examples:

$\angle ABC$ and $\angle DBC$ are coterminal because they are both $50^\circ$.

$\angle ABC$ and $\angle DBC$ are coterminal because $410^\circ\equiv50^\circ\pmod{360^\circ}$

$\angle ABC$ and $\angle DBC$ are coterminal because $-312^\circ\equiv48^\circ\pmod{360^\circ}$

This works for any angle system and in your case this is radians. To find coterminal angles you have to find angular solutions to this equivalence
$$\angle DBC \equiv \angle ABC \pmod{\angle S}$$
$\angle S$ is $2\pi$ for radians and $360^\circ$ for degrees.

So finally all you have to do is add or subtract $2\pi$.
1)
$$\frac\pi4+2\pi=\frac\pi4+\frac{8\pi}4=\frac{9\pi}4$$
$$\frac\pi4+4\pi=\frac\pi4+\frac{16\pi}4=\frac{17\pi}4$$
$$\frac\pi4-2\pi=\frac\pi4-\frac{8\pi}4=-\frac{7\pi}4$$
2)
$$\frac{5\pi}3+2\pi=\frac{5\pi}3+\frac{6\pi}3=\frac{11\pi}3$$
$$\frac{5\pi}3+4\pi=\frac{5\pi}3+\frac{12\pi}3=\frac{17\pi}3$$
$$\frac{5\pi}3-2\pi=\frac{5\pi}3-\frac{6\pi}3=-\frac{\pi}3$$
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