Lutasin ang y=2cos(1/2x-pi/2)

$$y = 2 \cos ( \frac { 1 } { 2 } x - \frac { \pi } { 2 } )$$

I-solve ang x (complex solution)

$$x=-2i\ln(\frac{\sqrt{y^{2}-4}+y}{2})+4\pi n_{1}+\pi \text{, }n_{1}\in \mathrm{Z}$$

$$x=-2i\ln(\frac{-\sqrt{y^{2}-4}+y}{2})+4\pi n_{2}+\pi \text{, }n_{2}\in \mathrm{Z}$$

I-solve ang y (complex solution)

$$y=e^{\frac{ix-\pi i}{2}}+e^{\frac{-ix+\pi i}{2}}$$

I-solve ang x

$$x=-2\arccos(\frac{y}{2})+4\pi n_{1}+\pi \text{, }n_{1}\in \mathrm{Z}$$

$$x=2\arccos(\frac{y}{2})+4\pi n_{2}+\pi \text{, }n_{2}\in \mathrm{Z}$$

I-solve ang y

$$y=2\cos(\frac{x-\pi }{2})$$