When you solve an equation like sin x = 0,5 why do you have to write both solutions and not just +- 30 + n * 360?

Question

Violet Anderson · Accepted Answer

Mostly because #sin(-30^@) != 0.5#

The solutions to #sinx=0.5# (for angles, in degrees) are

#-690^@, -330^@, 30^@, 390^@, 750^@# --that is #30^@ +n360^@#

and

#-570^@, -210^@, 150^@, 510^@, 870^@# --that is #150^@ +n360^@#

Anna Andrews · Answer

undefined When solving equations like $\sin(x) = 0.5$, you typically need to find all solutions within a specified interval. In this case, the interval is usually taken to be from $0$ to $360$ degrees or $0$ to $2\pi$ radians.

Since the sine function is periodic, it repeats its values every $360$ degrees or $2\pi$ radians. Therefore, when finding solutions, you should consider all possible repetitions of solutions within this interval.

Using $ \pm 30 + n \times 360 $ gives you only one solution set, but it doesn't cover all possible solutions within the specified interval. To find all solutions, you need to consider all possible repetitions of the solution within the interval, which is why you would write multiple solutions instead of just one.