Question

3. x- sin t, y- cos 2t

Answer 1

It is given that x and y are parametrically connected by the equations,

x=sint(1)

And,

y=cos2t(2)

Differentiate equation (2) with respect to t.

dy dt = d( cos2t ) dt dy dt =−2sin2t

Differentiate equation (1) with respect to t.

dx dt = d( sint ) dt dx dt =cost

We know that,

dy dx = dy dt dx dt

Substitute the value of dy dt and dx dt .

dy dx = −2sin2t cost dy dx = −2( 2sintcost ) cost dy dx =−4sint

Thus, the solution is dy dx =−4sint.