The variables $$$x$$$ and $$$y$$$ satisfy the differential equation  $$$ (1-\cos x) \frac{\mathrm{d} y}{\mathrm{~d} x}=y \sin x . $$$ It is given that $$$y=4$$$ when $$$x=\pi$$$. Sketch the graph of $$$y$$$ against $$$x$$$ for $$dummy$$

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m21_qp_32 Year：2021 Question No：4(b)

Answer:

Show a correct graph for $ 0<x<2 \pi \; $ with the maximum at $x=\pi$

Knowledge points:

3.3.1 understand the relationship of the secant, cosecant and cotangent functions to cosine, sine and tangent, and use properties and graphs of all six trigonometric functions for angles of any magnitude

Solution:

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The variables $$\(x\)$$ and $$\(y\)$$ satisfy the differential equation&nbsp; $$\( (1-\cos x) \frac{\mathrm{d} y}{\mathrm{~d} x}=y \sin x . \)$$ It is given that $$\(y=4\)$$ when $$\(x=\pi\)$$. Sketch the graph of $$\(y\)$$ against $$\(x\)$$ for $$dummy$$

Answer:

Knowledge points:

Solution:

Related Question

The variables $$\(x\)$$ and $$\(y\)$$ satisfy the differential equation $$\( (1-\cos x) \frac{\mathrm{d} y}{\mathrm{~d} x}=y \sin x . \)$$ It is given that $$\(y=4\)$$ when $$\(x=\pi\)$$. Sketch the graph of $$\(y\)$$ against $$\(x\)$$ for $$dummy$$