Question

Find `"dy"/"dx"` of the following function:

x = a cos³θ, y = a sin³θ

Answer 1

x = a cos³θ, y = a sin³θ

we have x = a cos³θ;  y = a sin³θ

Now, ∴ `"dx"/("d"theta) = - 3"a" cos^2theta sin theta and "dy"/("d"theta) = 3"a" sin^2theta cos theta`

Therefore `"dy"/"dx" = ("dy"/("d"theta))/("dx"/("d"theta))`

`= (3"a"sin^2theta cos theta)/(-3"a" cos^2theta sin theta)`

`= - (sin theta)/(cos theta)`

= - tan θ