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 \displaystyle\theta. \displaystyle\theta={{\tan}^{{-{1}}}{\left({5}\text{/}{12}\right)}}

Annette Arroyo 2021-01-04 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={tan1512}

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Expert Answer

lamusesamuset
Answered 2021-01-05 Author has 93 answers

Use the axis rotation formulas:
x=ucosθvsinθ
y=usinθ+vcosθ
From the given angle, we know that:
tanθ=512
From this tangent ratio, opp=5 and adj=12 so

hyp=(opp)2+(adj)2=52+122=169=13 so:
sinθ=opphyp=512
and
cosθ=adjhyp=1213
For x,
x=12u135v13
For y,
y=5u13+12v13

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