If the angle made by the tangent at the point ( x 0 , y 0 ) on the curve x = 12 ( t + sin t cos t ) , y = 12 ( 1 + sin t ) 2 , 0 < t < 2 π , with the positive x -axis is 3 π , then y 0 is equal to

Given equation of curve x = 12 ( t + sin t cos t ) , y = 12 ( 1 + sin t ) 2 Differentiate w.r.t ' t ', d t d x = 12 ( 1 + cos 2 t − sin 2 t ) d t d x = 12 ( 1 + cos 2 t ) and d t d y = 24 ( 1 + sin t ) cos t d x d y = 1 + cos 2 t 2 ( 1 + sin t ) × cos t

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsMedium2 minPYQ_2024

MathematicsMediumsingle choice

If the angle made by the tangent at the point $(x_{0}, y_{0})$ on the curve $x = 12 (t + sin t cos t), y = 12$ $(1 + sin t)^{2}, 0 < t < \frac{π}{2}$ , with the positive x -axis is $\frac{π}{3}$ , then $y_{0}$ is equal to

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Given equation of curve $x = 12 (t + sin t cos t), y = 12 (1 + sin t)^{2}$ Differentiate w.r.t ' $t$ ', $\frac{d x}{d t} = 12 (1 + cos^{2} t - sin^{2} t) \frac{d x}{d t} = 12 (1 + cos 2 t) and \frac{d y}{d t} = 24 (1 + sin t) cos t \frac{d y}{d x} = \frac{2 ( 1 + sin t ) \times cos t}{1 + cos 2 t}$

Stream:BITSATSubject:MathematicsTopic:Application of DerivativeSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: PYQ_2024

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