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From Förberedande kurs i matematik 1

Apart from the fact that there is a 5x, this is a normal trigonometric equation of the type siny=a. If we are only interested in solutions which satisfy 05x2, then a sketch of the unit circle shows that there are two such solutions, 5x=4 and the reflectionally symmetric solution 5x=−4=34.

All of the equation's solutions are obtained from all values of 5x which differ by a multiple of 2 from either of these two solutions,

5x=4+2nand5x=43+2n

where n is an arbitrary integer.

If we divide both of these by 5, we obtain the solutions expressed in terms of x alone,

x=20+52nandx=203+52n

where n is an arbitrary integer.