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 find the equation  of the normal to the curve x=cost y=sint at  t=pi/4

 Dec 20, 2018
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We need to find the slope of the line

 

dy/dx =   dy/dt  /  dx/dt  =  cost / - sin t  =   - cot t

 

At  t = pi/4, the slope is    - cot (pi/4)  =  - 1

 

The normal line will have a slope of 1

 

The point is given by   ( cos pi/4, sin pi/4) =  (  sqrt (2)/2, sqrt (2)/2 )

 

So....the equation of the tangent lne is

 

y = 1 (x - sqrt (2) /2 )  +  sqrt(2)/2 

 

y =  x

 

Here's the  graph :

 

 

cool cool cool 

 Dec 20, 2018
edited by CPhill  Dec 20, 2018

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