If x = a(θ + θ θ) and y = a(θ - θ θ) , then at θ = π/4 , which of the following is true? - Mathematics MCQ Mathematics Mock Test - 11 2026 | ExamTest.live

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1 mark

If x = a (cos θ + θ sin θ) and y = a (sin θ - θ cos θ), then at θ = \frac{π}{4}, which of the following is true?

Solution & Step-by-step Explanation

Given parametric equations: \frac{d x}{d θ} = a (- sin θ + sin θ + θ cos θ) = a θ cos θ \frac{d y}{d θ} = a (cos θ - (cos θ - θ sin θ)) = a θ sin θ \frac{d y}{d x} = \frac{d y / d θ}{d x / d θ} = \frac{a θ s i n θ}{a θ c o s θ} = tan θ At θ = \frac{π}{4}, \frac{d y}{d x} = tan (\frac{π}{4}) = 1 .

Try it yourself before checking the explanation above.

If x = a (cos θ + θ sin θ) and y = a (sin θ - θ cos θ), then at θ = \frac{π}{4}, which of the following is true?

\frac{d y}{d x} = 1

\frac{d ^{2} y}{d x ^{2}} = \frac{8 2}{aπ}

\frac{d y}{d x} = - 1

\frac{d ^{2} y}{d x ^{2}} = - \frac{8 2}{aπ}

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