Lösung 4.4:2d

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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,

Vorlage:Displayed math

where n is an arbitrary integer.

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

Vorlage:Displayed math

where n is an arbitrary integer.