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2*pi is one complete revolution, i.e. 360 degrees. Sin of 2*pi = sin 360º = 0
sin(pi) = 0
Do you mean Sin(pi/2) = 1 or [Sin(pi)] /2 = 0.0274....
(cos(pi x) + sin(pi y) )^8 = 44 differentiate both sides with respect to x 8 ( cos(pi x) + sin (pi y ) )^7 d/dx ( cos(pi x) + sin (pi y) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (-sin (pi x) pi + cos (pi y) pi dy/dx ) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (pi cos(pi y) dy/dx - pi sin (pi x) ) = 0 cos(pi y) dy/dx - pi sin(pi x) = 0 cos(pi y) dy/dx = sin(pi x) dy/dx = sin (pi x) / cos(pi y)
sin(pi) = 0 so 4*sin(pi) = 0 so Y = 0