Key to "Find the linear equations that can be used..."

Brennan Flores

Answered question

2021-08-19

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.

$θ = \frac{π}{3}$

Bentley Leach

Skilled2021-08-20Added 109 answers

Use the axis rotation formulas: $x = u \cos θ - v \sin θ$

$y = u \sin θ + v \cos θ$

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

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

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

For y, $y = u \sin (\frac{π}{3}) + v \cos (\frac{π}{3})$

$y = \sqrt{\frac{3 u}{2}} + \frac{v}{2}$

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?