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
ANSWERED
asked 2021-05-08

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 \(\theta\) . \(\theta=70^{\circ}\)

Answers (1)

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

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