Find the Linear Equations That Can Be Used to Convert $$\theta = \tan ^ { - 1 } \left( \frac { 4 } { 3 } \right)$$

Multiple Choice

Find the linear equations that can be used to convert an (x, y) equation to a (u, v) equation using the given angle of
rotation
- $$\theta = \tan ^ { - 1 } \left( \frac { 4 } { 3 } \right)$$

A) $x = \frac { 4 } { 5 } u - \frac { 3 } { 5 } v$
$y = \frac { 3 } { 5 } u + \frac { 4 } { 5 } v$

B) $\text { } \begin{aligned}x &=\frac{4}{3} u-\frac{4}{5} v \\y &=\frac{4}{5} u+\frac{4}{3} v\end{aligned}$

C) $$
$$\begin{array}{l}x=\frac{3}{5} u-\frac{4}{5} v \\y=\frac{4}{5} u+\frac{3}{5} v\end{array}$$

D) $x = \frac { 5 } { 3 } u - \frac { 5 } { 4 } v$
$y = \frac { 5 } { 4 } u + \frac { 5 } { 3 } v$