r^2=100cosθ ઉકેલો

$$r ^ { 2 } = 100 \cos \theta$$

r માટે ઉકેલો (જટિલ સમાધાન)

$$r=-10\sqrt{\cos(\theta )}$$

$$r=10\sqrt{\cos(\theta )}$$

θ માટે ઉકેલો (જટિલ સમાધાન)

$$\theta =-i\ln(\frac{\sqrt{r^{4}-10000}+r^{2}}{100})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =-i\ln(\frac{-\sqrt{r^{4}-10000}+r^{2}}{100})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}$$

r માટે ઉકેલો

$$r=10\sqrt{\cos(\theta )}$$

$$r=-10\sqrt{\cos(\theta )}\text{, }\exists n_{1}\in \mathrm{Z}\text{ : }\left(\theta \geq 2\pi n_{1}-\frac{\pi }{2}\text{ and }\theta \leq 2\pi n_{1}+\frac{\pi }{2}\right)$$

θ માટે ઉકેલો

$$\theta =-\arccos(\frac{r^{2}}{100})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =\arccos(\frac{r^{2}}{100})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }\frac{r^{2}}{100}\leq 1\text{ and }|r|\leq 10$$