Math, asked by rs0752052, 10 months ago

find the radius of curvature at x=π/2 to the curve y=4sinx-sin2x​

Answers

Answered by hukam0685
5

Answer:

Radius of curvature is

 K=\frac{4}{5 \sqrt{5} }  \\  \\

Step-by-step explanation:

To find the radius of curvature of the curve

y = 4 \: sinx - sin \: 2x \:

at point x = π/2

Step1: find y'

 \frac{dy}{dx}  =y^{'}= 4cos \: x - 2cos \: 2x \\  \\

Step2:Find y''

 \frac{ {d}^{2}y }{d {x}^{2} }  =y^{''}= - 4sin\: x  + 4 sin \: 2x \\  \\

Step3: Apply the formula

K =  \frac{ |y^{''}| }{ {(1 +  {y^{'}}^{2}) }^{ \frac{3}{2} } }  \\  \\   K=  \frac{ |4sin \: x + 4sin2x| }{ {(1 +  {( - 4cos \: x - 2cos \: 2x)}^{2}) }^{ \frac{3}{2} } } \:  \\  \\  K_{ x =  \frac{\pi}{2} }=  \frac{ |4sin \: \frac{\pi}{2}+ 4sin2\frac{\pi}{2}| }{ {(1 +  {( - 4cos \: \frac{\pi}{2} - 2cos \: 2\frac{\pi}{2})}^{2}) }^{ \frac{3}{2} } } \:  \\  \\  K= \frac{ |4(1)+ 4(0)|  }{ {(1 +  {( - 4(0) - 2( - 1))}^{2}) }^{ \frac{3}{2} } } \:  \\  \\ K= \frac{ |4|  }{ {(5) }^{ \frac{3}{2} } } \:  \\  \\ K=  \frac{4}{5 \sqrt{5} }  \\  \\

Hope it helps you.

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