Question Number 36739 by tawa tawa last updated on 04/Jun/18
$$\mathrm{If}\:\:\:\mathrm{x}\:=\:\mathrm{a}\left(\mathrm{1}\:−\:\mathrm{cos}\theta\right)\mathrm{i}\:\:+\:\:\mathrm{asin}\theta\:\mathrm{j} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{resultant}\:\mathrm{of}\:\mathrm{x}\:\mathrm{in}\:\mathrm{its}\:\mathrm{simplest}\:\mathrm{form}. \\ $$
Commented by prof Abdo imad last updated on 05/Jun/18
$${x}\:=\:\mathrm{2}{a}\:{sin}^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}}\right){i}\:\:+\mathrm{2}{asin}\left(\frac{\theta}{\mathrm{2}}\right){cos}\left(\frac{\theta}{\mathrm{2}}\right){j} \\ $$$$=\mathrm{2}{a}\:{sin}\left(\frac{\theta}{\mathrm{2}}\right)\left\{\:{sin}\left(\frac{\theta}{\mathrm{2}}\right){i}\:+{cos}\left(\frac{\theta}{\mathrm{2}}\right){j}\right\}\:\Rightarrow \\ $$$$\mid\mid{x}\mid\mid\:=\mathrm{2}\mid{asin}\left(\frac{\theta}{\mathrm{2}}\right)\mid\:. \\ $$
Commented by tawa tawa last updated on 07/Jun/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Commented by maxmathsup by imad last updated on 07/Jun/18
$${and}\:{you}\:{too}\:{sir}. \\ $$