Uttrycket asinx+bcosx

$$a\sin(\alpha) + b\cos(\alpha) = \left( \sqrt {a^2+b^2} \right)\sin(\alpha + x)$$

$$a\sin(\alpha) - b\cos(\alpha) = \left( \sqrt {a^2+b^2} \right) \sin(\alpha - x)$$

Detta gäller då:

$$a  > 0$$

$$b >  0$$

$$\tan(x) = \frac{b}{a}$$

$$0^\circ < x < 90^\circ$$