Question Number 140666 by john_santu last updated on 11/May/21
$${Find}\:{the}\:{coordinates}\:{of}\:\left(−\mathrm{2},\mathrm{0}\right)\: \\ $$$${when}\:{the}\:{axes}\:{are}\:{rotated}\:{counterclockwise} \\ $$$${through}\:{the}\:{angle}\:\mathrm{arcsin}\:\frac{\mathrm{4}}{\mathrm{5}}. \\ $$
Answered by bemath last updated on 11/May/21
$$\begin{cases}{\mathrm{x}'=\mathrm{x}\:\mathrm{cos}\:\theta−\mathrm{ysin}\:\theta}\\{\mathrm{y}'=\mathrm{xsin}\:\theta+\mathrm{ycos}\:\theta}\end{cases} \\ $$$$\begin{cases}{\mathrm{x}'=−\mathrm{2}\left(\frac{\mathrm{3}}{\mathrm{5}}\right)}\\{\mathrm{y}=−\mathrm{2}\left(\frac{\mathrm{4}}{\mathrm{5}}\right)}\end{cases}\:\rightarrow\left(\mathrm{x}',\mathrm{y}'\right)\:=\:\left(−\frac{\mathrm{6}}{\mathrm{5}},−\frac{\mathrm{8}}{\mathrm{5}}\right) \\ $$