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Question

# Find the curvature at the given point on the polar curve given.$r=1-2 \sin \theta, \text { where } \theta=\frac{\pi}{4}$

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Let us consider the equation of the polar curve $~~r=1-2\sin \theta.$ We will now evaluate the curvature of the plane curve at $~~\theta=\dfrac{\pi}{4}.$ Now from above given context, we have

$\kappa = \frac{|r^2+2r'^2-rr''|}{(r^2+r'^2)^{3/2}},$

where $~~\kappa~~$ denotes the curvature of the curve $~~r=1-2\sin \theta.$

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