Find the linear equations that can be used to convert

Brennan Flores 2021-08-19 Answered

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.

\(θ=\frac{π}{3}\)

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Expert Answer

Bentley Leach
Answered 2021-08-20 Author has 16954 answers

Use the axis rotation formulas: \(x=u\cosθ-v\sinθ\)

\(y=u\sinθ+v\cosθ\)

Substitute \(θ=\frac{π}{3}\). This is a special angle so we can find the exact values.

For x, \(x=u\cos \frac{π}{3}-v\sin \frac{π}{3}\)

\(x=\frac{u}{2}-\sqrt{\frac{3v}{2}}\)

For y, \(\displaystyle{y}={u} \sin{{\left(\frac{\pi}{{3}}\right)}}+{v} \cos{{\left(\frac{\pi}{{3}}\right)}}\)

\(\displaystyle{y}=\sqrt{{\frac{{{3}{u}}}{{2}}}}+\frac{v}{{2}}\)

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