Question

If x = sin θ, y = sin³ θ then `("d"^2"y")/"dx"^2  "at" theta = pi/2` is ______.

Options

• 3

• 6

• `1/6`

• `1/3`

Answer 1

If x = sin θ, y = sin³ θ then `("d"^2"y")/"dx"^2  "at" theta = pi/2` is 6.

Explanation:

We have, x = sin θ, y = sin³ θ

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

`= (3 sin^2 theta (cos theta))/(cos theta)`

`=> "dy"/"dx" = 3 sin^2 theta`

Now, `("d"^2"y")/"dx"^2 = 3(2 sin theta cos theta) ("d"theta)/"dx"`

= 3 (2 sin θ cos θ)`1/(cos theta) = 6 sin theta`

at `theta = pi/2, ("d"^2"y")/"dx"^2 = 6 sin (pi/2) = 6 xx 1 = 6`