Find dy/dx if y=(1+sin(t-1)), x=(1-sin(t+1))?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function y=(1+sin(t-1)) and x=(1-sin(t+1))

`dy/dx = (dy/dt)/(dx/dt)`

`dy/dt = cos (t-1)`

`dx/dt = -cos(t+1)`

`dy/dx = (dy/dt)/(dx/dt)`

= `(cos (t-1))/(-cos(t+1))`

= `-cos(t-1)/cos(t+1)`

The required derivative `dy/dx = -cos(t-1)/cos(t+1)`

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