Eliminate \theta from from \frac{x-k \sin \theta \cot \alpha}{k \cos \theta}=\frac{y-k

Adrian Cervantes

Adrian Cervantes

Answered question

2022-01-26

Eliminate θ from from
xksinθcotαkcosθ=ykcosθtanαksinθ=zc

Answer & Explanation

Addison Kirk

Addison Kirk

Beginner2022-01-27Added 5 answers

Write your line as
xksinθcotαkcosθ=zc  and  ykcosθtanαksinθ=zc
Manipulate the two equations into
cxk=ccotαsinθ+zcosθ
cyk=zsinθ+ctanαcosθ
so solving for sinθ,cosθ:
k(c2z2)sinθ=ctanαcxzcy
k(c2z2)cosθ=ccotαcyzcx
Now remember sin2θ+cos2θ=1

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