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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`
Solution
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
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