Question

Eliminate thita from the following : x = a cos³thita y = b sin³thita​

Answer 1

consider given equation,

x=acos3θ.(1)andy=asin3θ.(2)

From equation (1) and (2) to,

ax=cos3θanday=sin3θ

(ax)31=cosθand(ay)31=sinθ

Then,

cosθ=(ax)31.(3)andsinθ=(ay)31.(4)]

Squaring both side equation (3) and (4), we get

cos2θ=(ax)32.(5)andsin2θ=(ay)32(6)]

Adding equation (5) and (6) to,

cos2θ+sin2θ=(ax)32+(ay)32]

[1=(ax)32+(ay)32]

[(ax)3