Find the linear equations that can be used to convert

Tabansi 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. 

\(θ=70^∘\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

hajavaF
Answered 2021-08-20 Author has 14501 answers

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

\(vy=u\sinθ+v\cosθ\)

Substitute \(θ=70^∘\). This is not a special angle so we use a calculator to approximate.

For x, \(x=u\cos70^∘-v\sin70^∘\)

\(x=0.342u-0.940v\)

For y, \(y=u\sin70^∘+v\cos70^∘\)

\(y=0.940u+0.342v\)

Have a similar question?
Ask An Expert
8
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...