y=acosθ(4sinēθ-1)
can anybody please help me trace this curve btw can you also tell me its name because this should also have a physical significance please help me its my mathematics assignment and i've tried much over it.
If by "trace this curve" you mean "graph it", then you can
first find the functions "zeros", if any, that is, the values of θ s.t. y = 0. (shouldn't be too difficult to fator)
then you can take its derivative, then find the critical points such that y' = 0. then find the sign between each interval to see where it's increasing or decreasing
then you can take its second derivative, find the critical points such that y'' = 0. then find the sign between each interval to see where it's concave up and concave down.
this should give you enough information to draw a graph.