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

Annette Arroyo

Answered question

2021-01-04

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}

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2021-01-05Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?