Find the perpendicular distance from the origin to the line joining the points

(cosθ, sinθ) and (cosϕ, sinϕ)

Asked by Pragya Singh | 1 year ago |  89

##### Solution :-

The equation of the line joining the points (cosθ,sinθ) and (cosϕ,sinϕ) is given by,

y−sinθ=cosϕ−cosθsinϕ−sinθ​(x−cosθ)

x(sinϕ−sinθ)+y(cosϕ−cosθ)+cosθsinϕ

−cosθsinθ−sinθcosϕ+sinθcosθ=0

x(sinθ−sinϕ )+y(cosϕ−cosθ)+sin(ϕ−θ)=0

Therefore, the perpendicular distance (d) of the given line from point (0,0) is

$$\dfrac{∣sin(ϕ−θ)∣}{\sqrt{2(1-cos(ϕ-θ}))}$$

$$\dfrac{∣sin(ϕ−θ)∣}{\sqrt{2(2sin^2(\dfrac{ϕ-θ}{2}))}}$$

$$\dfrac{∣sin(ϕ−θ)∣}{2(2sin^2(\dfrac{ϕ-θ}{2}))}$$

$$\dfrac{∣sin(ϕ−θ)∣}{2sin(\dfrac{ϕ-θ}{2})}$$

Answered by Pragya Singh | 1 year ago

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