Question

find the acute angle between the tangent line r=3+3cosθ at the pole

Answer 1

pareho tayo ng assignment

Answer 2

If you write it as a parametric curve, you get:\[x(\theta)=r(\theta)\cos\theta\]\[y(\theta)=r(\theta)\sin\theta\]So for your curve this becomes:\[x(\theta)=(3+3\cosθ)\cosθ\]\[y(θ)=(3+3\cosθ)\sinθ\]If you mean by "pole" the point (0, 0), the tangent line there can be found by this limit:\[\lim_{θ \rightarrow \pi}\frac{ y(θ)-0 }{ x(θ)-0 }=\lim_{θ \rightarrow \pi}\frac{ (3+3\cosθ)\sinθ }{ (3+3\cosθ)\cosθ }=\lim_{θ \rightarrow \pi}\frac{ \sinθ }{ \cosθ }=\lim_{θ \rightarrow \pi}\tanθ=0\]And this means the tangent line in (0,0) is the x-axis.

Answer 3

This is the curve, I guess...

Answer 4

yes..but i need to find the acute angle

Answer 5

I don't know what you mean by that. Could you explain with a drawing, perhaps?

Answer 6

\[\frac{ d y }{ d \theta } = \frac{ f \prime (\theta) \sin \theta + f(\theta)\cos \theta }{ f \prime (\theta)\cos \theta -f prim \sin \theta }\]