Question

# Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation θ. θ=π/3

Transformations of functions

Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation $$\theta$$ . $$\theta=70^{\circ}$$

2021-05-09

Use the axis rotation formulas: $$\displaystyle{x}={u} \cos{\theta}-{v} \sin{\theta}$$

$$\displaystyle{v}{y}={u} \sin{\theta}+{v} \cos{\theta}$$

Substitute $$\displaystyle\theta={70}^{\circ}$$. This is not a special angle so we use a calculator to approximate.

For x, $$\displaystyle{x}={u}{ \cos{{70}}^{\circ}-}{v}{ \sin{{70}}^{\circ}}$$

x=0.342u-0.940v

For y, $$\displaystyle{y}={u}{ \sin{{70}}^{\circ}+}{v}{ \cos{{70}}^{\circ}}$$​​​​​​​

y=0.940u+0.342v