Question

The slope of the tangent to the curve x = sin θ and y = cos 2θ at θ = `π/6` is ______.

Options

• `-2sqrt3`

• `(-2)/sqrt3`

• −2

• `-1/2`

Answer 1

The slope of the tangent to the curve x = sin θ and y = cos 2θ at θ = `π/6` is −2.

Explanation:

x = sin θ, y = cos θ, at θ = `π/6`

Differentiating w.r.t. θ,

`(dy)/dx` = `((dy)/(dθ))/((dx)/(dθ))`

= `(-sin 2theta × 2)/cos theta`

= `(-2 × 2sinθ. cosθ)/cosθ`

= −4 sinθ

= −4 sin `π/6`

= `-4 × 1/2`

= −2