# Find the linear equations that can be used to convert

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.

$$θ=70^∘$$

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hesgidiauE

Use the axis rotation formulas:

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, $$x=u\cos7^0∘-v\sin70^∘$$

$$x=0.342u-0.940v$$

For y, $$y=u\sin7^0∘+v\cos70^∘$$

$$y=0.940u+0.342v$$