A curve has parametric equations x= z-cos z , y=sin z , for -pi<z<pi. Find the coordinates of the point at which the gradient of this curve is zero?

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Answer 1 · 2015-08-26T14:23:27

#(pi/2, 1)#

For #-pi < z < pi#

#x= z-cos z # #" "# and #" "##y=sin z#.

#dx/dz = 1+sinz# #" "# and #" "##dy/dz = cos z#.

So

#dy/dx = cosz/(1+sinz)#

#cosz = 0# at #z = -pi/2 " and " pi/2#

But #dy/dx# does not exist at #z = -pi/2#.

When #z = pi/2#, we get #(x,y) = (pi/2, 1)#