Every Solution

With no domain, an equation has infinitely many answers, and you write them all at once. $\sin\left(x\right) = \frac{\sqrt{2}}{2}$ has 45° and 135° in one turn, and every full turn adds the same two again. So every solution is

$$x = 45^{\circ}+360^{\circ}\cdot k$$

$$x = 135^{\circ}+360^{\circ}\cdot k$$

where k is any integer: …, −2, −1, 0, 1, 2, …. k = 1 gives 405° and 495°; k = −1 gives −315° and −225°. Each line is called a family. Find the answers in one turn, then add 360°k to each.