Q.1 (v) The slope of the tangent to the curve x = sinθ and y = cos 2θ at θ = π/6 is _____. A. -2√(3) B. -2/√(3) C. -2 D. -1/2

Answer: C. -2 Answer: (c) -2 dx/dθ = cosθ , dy/dθ = -2sin 2θ , so dy/dx = -2sin 2θ/cosθ = -4sinθcosθ/cosθ = -4sinθ . At θ = π/6 : slope = -4 × 1/2 = -2 .

The slope of the tangent to the curve \(x = \sin\theta\) and \(y = \cos 2\theta\) at \(\theta = \frac{\pi}{6}\) is _____.

Q.1 (v) The slope of the tangent to the curve \(x = \sin\theta\) and \(y = \cos 2\theta\) at \(\theta = \frac{\pi}{6}\) is _____.

A. \(-2\sqrt{3}\)

B. \(\frac{-2}{\sqrt{3}}\)

C. \(-2\)

D. \(-\frac{1}{2}\)

Doubtly Asked 29 Oct 2026 Board exam · March 2024 hsc 12th Save WhatsApp Report

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Answer: C. \(-2\)

Answer: (c) \(-2\)

\(\frac{dx}{d\theta} = \cos\theta\), \(\frac{dy}{d\theta} = -2\sin 2\theta\), so \(\frac{dy}{dx} = \frac{-2\sin 2\theta}{\cos\theta} = \frac{-4\sin\theta\cos\theta}{\cos\theta} = -4\sin\theta\).

At \(\theta = \frac{\pi}{6}\): slope \(= -4 \times \frac{1}{2} = -2\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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The slope of the tangent to the curve \(x = \sin\theta\) and \(y = \cos 2\theta\) at \(\theta = \frac{\pi}{6}\) is _____.

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