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Example 34 - Find dy/dx, if x = a cos theta, y = a sin - Examples

Example 34 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Example 34 Find 𝑑𝑦/𝑑π‘₯ , if π‘₯ = π‘Ž cosβ‘πœƒ, 𝑦 = π‘Ž sin ΞΈ.Here 𝑑𝑦/𝑑π‘₯ = (𝑑𝑦/π‘‘πœƒ)/(𝑑π‘₯/π‘‘πœƒ) Calculating π’…π’š/π’…πœ½ 𝑦 = π‘Ž sin ΞΈ 𝑑𝑦/π‘‘πœƒ = 𝑑(π‘Ž sin πœƒ)/π‘‘πœƒ 𝑑𝑦/π‘‘πœƒ = 𝒂 π’„π’π’”β‘πœ½ Calculating 𝒅𝒙/π’…πœ½ 𝑦 = π‘Ž cos ΞΈ 𝑑𝑦/π‘‘πœƒ = 𝑑(π‘Ž cos πœƒ)/π‘‘πœƒ 𝑑𝑦/π‘‘πœƒ = βˆ’π’‚ π’”π’Šπ’β‘πœ½ Now, 𝑑𝑦/𝑑π‘₯ = (𝑑𝑦/π‘‘πœƒ)/(𝑑π‘₯/π‘‘πœƒ) 𝑑𝑦/𝑑π‘₯ = (π‘Ž cos⁑θ)/(βˆ’π‘Ž sin⁑θ ) π’…π’š/𝒅𝒙 = βˆ’πœπ¨π­β‘π›‰

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.