dai tyo calculator ko wrong xaena baru tyo solution chahi incomplete ho answer +/- dubai hunu parne ho cos-1(x) ko range le garda testo vako ho graph plot garera herne vane pani -1 to -0.5 ko interval ma -ve slope xa ani -0.5 to 0.5 ma +ve slope ani 0.5 to +1 ma feri -ve slope so, tya +/- duitai sign huna parne ho cos-1(cosθ) =θ is valid only if θ∈[0,π] kina vane cos-1x ko range 0 to π hunxa. cos-1(cosθ) = 2π - θ if θ∈[π,2π] cos-1(cosθ) = θ - 2π if θ∈[2π,3π] tyo solution ko yo step incomplete xa cos-1(cos(3θ)) = 3θ valid huna 3θ ∈ [0,π] => θ∈[0,π/3] And, cos-1(cos(3θ)) =2π - 3θ if 3θ ∈ [π,2π] => θ∈[π/3,2π/3] tapaile linu vako value x=0.2 or, cosθ=0.2 ( As x=cosθ by assumption) or,θ=78.46 degree ∈[π/3,2π/3] so, x=0.2 lida, cos-1(cos(3θ)) =2π - 3θ hunxa so, y= 2π - 3θ y' = - 3 dθ/dx = 3/(√ 1-x^2) ( +ve)
Conclusion: Tyo solution garda hamle tin ta interval ko laagi vanera garna parxa that will give both -ve and +ve slope.
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dai tyo calculator ko wrong xaena baru tyo solution chahi incomplete ho answer +/- dubai hunu parne ho
cos-1(x) ko range le garda testo vako ho
graph plot garera herne vane pani -1 to -0.5 ko interval ma -ve slope xa ani -0.5 to 0.5 ma +ve slope ani 0.5 to +1 ma feri -ve slope
so, tya +/- duitai sign huna parne ho
cos-1(cosθ) =θ is valid only if θ∈[0,π] kina vane cos-1x ko range 0 to π hunxa.
cos-1(cosθ) = 2π - θ if θ∈[π,2π]
cos-1(cosθ) = θ - 2π if θ∈[2π,3π]
tyo solution ko yo step incomplete xa
cos-1(cos(3θ)) = 3θ valid huna 3θ ∈ [0,π] => θ∈[0,π/3]
And,
cos-1(cos(3θ)) =2π - 3θ if 3θ ∈ [π,2π] => θ∈[π/3,2π/3]
tapaile linu vako value x=0.2
or, cosθ=0.2 ( As x=cosθ by assumption)
or,θ=78.46 degree ∈[π/3,2π/3]
so,
x=0.2 lida,
cos-1(cos(3θ)) =2π - 3θ hunxa
so,
y= 2π - 3θ
y' = - 3 dθ/dx = 3/(√ 1-x^2) ( +ve)
Conclusion: Tyo solution garda hamle tin ta interval ko laagi vanera garna parxa that will give both -ve and +ve slope.
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