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=tan^−1(5/12)

e1s2kat26

e1s2kat26

Answered question

2021-05-12

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=tan1(5/12)

Answer & Explanation

Neelam Wainwright

Neelam Wainwright

Skilled2021-05-13Added 102 answers

Use the axis rotation formulas: x=ucosθvsinθ

y=usinθ+vcosθ

From the given angle, we know that:

tanθ=5/12

From this tangent ration, opp=5 and adj=12 so hyp=(opp)2+(adj)2=52+122=169=13 so:

sinθ=opp/hyp=5/12

and

cosθ=adj/hyp=12/13

For x,

x=12u/13-5v/13

For y,

y=5u/13+12v/13

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