Loading Documentfor the curve r = 1 + cosθ when is the tangent horizontal or c vertical
sol:
x=rcosθ→x=(1+cosθ)cosθy=rsinθ→y=(1+cosθ)sinθdθdy=2cosθ2+cosθ−1dθdx=−sinθ(2cosθ+1)dθdy=0,dθdx=0⟹2cosθ2+cosθ−1=0cosθ=u⟹2u2+u−1u=−1±√(1)2−4(2)(−1)/2(2)u=−1±3/4⟹cosθ=21,−1cosθ=−21⟹32π,34πThe tangent is horizontal at⟹3π,π, 5πThe tangent is perpendicular to⟹32π,π,34π,2π